ejercicios resueltos de el algebra de baldornjxbcjhbj

5/3/2015 Ejerciciosresueltosdeelalgebradebaldor

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1.EJERCICIO11.UnadeudaseexpresaensentidoEJERCICIO3negativo.LuegoinicalmenteelestadoeconmicodePedroes60bs.Alrecibir320bs.Aumentasucapital1.+32m16mtantosbs.comoharecibidoentonces2.+10m4mlaoperacinquedaexpresadacomoseindica3.5085=35m60+320=+260bs.4.6{11=66m2.1.1701.515=345sucres5.86=48m3.200+56189=+$6796=+54m4.6651.178+2.280=+437soles5.2015+4075=$306.400{2=+800mcorredor400{3=1.200myo6.67+7216+2=$97.Los40piesdelongituddelposte7.200788193+4159=70colonesserepartenasi:15piesquesobresalen8.456679+20010=0seasumenensentidopositivo.25piesqueseencuentranenterrados.seasumenensentidonegativo.Alintroducir3piesms,seadicionanEJERCICIO2alosqueestanbajoelsueloysedebendescontardelosqueestanporencima.1.1215=3!Aritmticamentesignifica:2.3+86=1!40=15+25253=28pies3.15(3)=15+3=18!+153=+12pies()4.8+5=8+5=13!5.4+7+211=6!8.5552=+3m9.32+15=17m6.8+4{1=8+4=4!7am10.3547=12m8+4{2=8+8=0!8am8+4{5=8+20=+12!11am11.39+56=+17m12.905836=4m7.12{2=14=5!10am13.7230{1=7230=+42m12{3=16=7!11am7230{2=7260=+12m12{3+3{1=16+3=4!12am7230{3=7290=18m12{3+3{3=16+9=+2!2pm7230{4=72120=48m8.56+7=49!14.120(60){1=120+60=60Km9.71+5=66!long120(60){2=120+120=015+(5)=20!lat.120(60){3=120+180=+60Km120(60){4=120+240=+120Km10.18+3=+21!long654=+61!lat.11.75+135=+60aos2.EJERCICIO7.27.11a+8a+9a+11a=39a1.x+2x=3x28.mx+1+3mx+1+4mx+1+6mx+1=14mx+12.8a+9a=17a29.x2y8x2y9x2y20x2y=38x2y3.11b+9b=20b30.3am5am6am9am=23am4.b5b=6b1114+2+1+8155.8mm=9m31.a+a+a+a=a=a248886.9m7m=16m21118+10+2+12132.ax+ax+ax+ax=ax=ax7.4ax+5ax=9ax52102020208.6ax+1+8ax+1=14ax+133.0,5m+0,6m+0,7m+0,8m=2,6m9.mx+15mx+1=6mx+111134.abababab7142810.3ax2ax2=4ax242128355=ab=ab=ab111+122828411.a+a=a=a=a2222231113316ab+ab7
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35.xyx3yx3yxy3691212.ab+ab==ab5101010246433373=xy=xy3636112+13113.xy+xy=xy=xy=xy3666236.ab2+ab2+7ab2+9ab2+21ab2=39ab21414537.mm8m7m3m=20m14.xyxy==xy=xy555538.xa+18xa+14xa+15xa+1xa+1=19xa+1521203223215.aba2b=ab=ab1111168242439.a+a+a+a+a234567871530+20+15+12+10872916.a8a=8a=8a=a=a=a60602017.8a+9a+6a=23a1111118.15x+20x+x=36x40.ababababab36212919.7m8m9m=24m126183443=ab=ab363620.a2ba2b3a2b=5a2b21.ax+3ax+8ax=12ax22.5ax+13ax+15ax+1=13ax+1EJERCICIO8126+3+41323.a+a+a=a=a1.8a6a=2a236621641112.6a8a=2a24.xxx=x=x36663.9ab15ab=6ab132+3+101534.15ab9ab=6ab25.ax+ax+ax=ax=ax=ax510101025.2a2a=0359101223126.7b+7b=026.axaxax=ax=222ax4612127.14xy+32xy=18xy3.8.25x2y+32x2y=7x2y5m+17m+1107m+13m+11m+135.aa=a=a=a612121249.40x3y51x3y=11x3y12121211236.4aa=a=a210.m2n+6m2n=5m2n33311.15xy+40xy=25xy320+31737.5mn+mn=mn=mn12.55a3b281a3b2=26a3b244413.x2y+x2y=038.8ax+2bx+325ax+2bx+3=17ax+2bx+314.9ab2+9ab2=07mnmn7+8mn1mn39.ab+ab=ab=ab88815.7x2y7x2y=040.0,85mxy0,5mxy=0,35mxy16.101mn+118mn=17mn17.502ab405ab=97ab18.1024x+1018x=6xEJERCICIO919.15ab+15ab=0132311.9a3a+5a=11a20.aa=a=a24442.8x+9xx=0313213.12mn23mn5mn=16mn21.aa=a=a42444.x+19x18x=052521052525.19m10m+6m=15m22.abab=ab=ab61212126.11ab15ab+26ab=042928+92127.5aX+9aX35aX=31aX23.xy+xy=xy=xy71414148.24aX+215aX+2+39aX+2=035310724.amam=am=am212+1308488y+yy=y=y=09.333335+3225.am+am=am=am31112+5101755510.m+mm=m=m5422020572021126.mnmn=mn=mn3213+2823682424ab+a2ba2b=ab=a2b11.84883211+32827.ab+ab=ab=a2b212.a+8a+9a15a=a11111113.7ab11ab+20ab31ab=15ab28.3,4a4b35,6a4b3=2,2a4b314.25x250x2+11x2+14x2=029.12yz+3,4yz=2,2yz,15.xy8xy19xy+40xy=12xy30.4ax2ax=2ax16.7ab+21abab80ab=53ab31.8ax+1+8ax+1=017.25xy2+11xy2+60xy282xy2=36xy232.25ma132ma1=7ma118.72ax+87ax101ax+243ax=157ax33.xa+1+xa+1=019.82bx71bx53bx+206bx=01m21m21+2m21m220.105a3464a3+58a3+301a3=034.a+a=a=a42444.1111xx+xx=3020+1512x=13xEJERCICIO1021.23456060111144+21122.yy+yy=y=y1.7a+6a9b4b3361212127a+6a=13a9b4b=13b321212=13a13b23.5ab6ab+3abab2185+10302722.a+bcbc+2ca=ab=abaa=0bb=0cc+2c=03030=052123224.6ab6ab+ab8ab23.5x11y9+20x1y204+2492935x+20x=25x11yy=12y91=10=ab=ab2=ab2=25x12y102424825.a+8a11a+15a75a=64a4.6m+8n+5mn6m1126.7c+21c+14c30c+82c=80c6mm6m=13m8nn=7n511=6=13m+7n627.mn+14mn31mnmn+20mn=mn28.a2y7a2y93a2y+51a2y+48a2y=05.a+b+2b2c+3a+2c3ba+3a=2ab+2b3b=02c+2c=029.a+aa+a3a+6a=3a=2a1271x+xx+xx30.23626.81x+19y30z+6y+80x+x25y3+47+363181x+80x+x=019y+6y25y=030z=x=x=x662=30z3157.15a26ab8a2+205ab31+a2ab31.2x+4x+4x+x6x15a28a2+a2=8a248+18+6+2420205=x=x=x6ab5abab=12ab2031=1124246=8a12ab11232.7ax30ax41ax9ax+73ax=08.3a+4b6a+81b114b+31aab33.ax+1+7ax+111ax+120ax+1+26ax+1=ax+13a6a+31aa=21a34.a+6a20a+150a80a+31a=88a4b+81b114bb=30b35.9b11b17b81bb+110b=9b=21a30b36.a2b+15a2b+a2b85a2b131a2b+39a2b=162a2b9.71ab84ab+50ab+84ab45ab+18ab3423423337.84m2x501m2x604m2x715m2x+231m2x+165m2x71a3b+50a3b45a3b+18a3b=48a3b=1340m2x84a4b2+84a4b2=0532232132532=48a3b38.ab+ababab+4a3b2634820+16615+96321113210.a+bc+8+2a+2b192c3a33b+3c=ab=ab2424a+2a3a=2ab+2b3b=0=3732ab=45a3b2c2c+3c=08193=1488=2a1439.40a81a+130a+41a83a91a+16a=28a40.21ab+52ab60ab+84ab31abab23ab=05.11.m+71mn14m65mn+mm115m+6m223223m+6m=7m333m14mm115m2=129m22227165mn=6mnmn=7m3129m2+6mn12.xyxy+xy8xyxy10+xy7xy9+21xyy+50432242323243x4y8x4y+21x4y=14x4yx3y2+x3y27x3y2=7x3y2x2yx2y=0y3109+50=31=14xy7xyy+31432313.5ax+13bx+28cx+35ax+150+4bx+265bx+2+90+cx+3+7cx+38cx+3+cx+3+7cx+3=03bx+2+4bx+2bx+2=05ax+15ax+1=05065+90=25=2514.am+2xm+35+83am+2+5xm+36+am+25xm+3xm+3+5xm+35xm+3=xm+3am+23am+2+am+2=am+25+86=3m+3m+2=xa315.0,3a+0,4b+0,5c0,6a0,7b0,9c+3a3b3c0,3a0,6a+3a=2,7a0,4b0,7b3b=3,3b0,5c0,9c3c=3,4c=2,7a3,3b3,4c11313116.a+b+2a3bab+234642132+8371121811731321a+2aa=a=ab3bb=b=b==2444366642447171=ab+464321117.m2mn+m2mn+2mn2m251033216+120213161+61m+m22m2=m=m22mnmn+2mn=mn=mn51010103331321=mmn10318.3a2+1ab5b2+21a23ab+1b21b22ab342646332729+282192132389a+a=a=aabab2ab=ab=ab43121224445212125+12262b+bb=b=b=b2663661929=aabb21246.322119.0,4xy+31+xy0,6y3x2y0,2xy2+y3628542222323162142,,0,4x2yx2y=xy=0xy0,2xy2=xy=xy=0,175xy25588812,4+13,1430,6y3+y3=y=y=0,35y3316=25444=0,175xy20,35y3+2537m23m11m21am1b+ab0,2am1+bm220.255052553m13m13+155m113m17m21m21m272+10m21m2a+a0,2am1=a=abb+b=b=b255252550255505013m11m2=a+b2550EJERCICIO11Pararesolverlosproblemasdel1al18lasliteralestomanlossiguientesvalores:a=1b=2c=3m=1/2n=1/3p=1/41.3ab=3{1{2=64a4{1422.5a2b3c=5{12{23{3=5{8{3=12012.===3bc3{2{3189211423.bmn=2{{==222363 1 15{22{ 20{5bm22 2 4=5=6013.==23 1 1 111614.24mnp=24 {=6{{==111123np 2 3 427410818{341212324232421 218133333{8245.abm={1{2{ ={4{=={233 2 3824314.4b6=4=4=4==122222{918673272 1 11891118963c{36.cpm={33{ {={{==33331212 4 21216238412812{23 1 1 111117.mnp= {={{=2m2=1=1=3bca 2 3 4427443215.=n2 1 211 5b1c2521 1 32515 3 938.a{m={1{ ={=66 2 621211249.2bc2=2{2{32=4{9=36=624mn24{{416.=23=6=2{n2p22 1 1 2111132{ 2{{2{10.4m{12bc=4{{12{2{32=2{3216=2{6=12322 3 4 9161444411184===2411.mn{8ab={{8{14{23={64==4311236632{1267.3{364{23{3617.3{64bc=336=3{364{8{729=3{3373.248=3{72=2162m12{23313433318.{apb2{1{{22{{15=54=54=5=5=5=6=2332503{31253{5157525{125bm3{3125{2{13{322222222EJERCICIO12Pararesolverlosproblemasdel1al18lasliteralestomanlossiguientesvalores:a=3b=4c=1/3d=1/2m=6n=1/41.a22ab+b2=322{3{4+42=924+16=11114+12+92522 1 11 1 2.c+2cd+d= +2{{+ =++==22 3 32 2 9343636ab343.+=+=9+8=17cd11321cm62272+6644.+2=3+2=24+2==dn1133324a2b2m2324262916365.+=+=+=38
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+6=13263263263131111110+546.cb+2d={{4+2{=2+1==525322555113{4{abacbd3{432=12+12=48+21=144+61=149=492+=+37.ndm1161163334242114+1+12178.b+n+6m=4++6{6=2++6===821422211111111216+1139.c3ad16b+n8d={3{3{16{4+{8{={3{16+{2=18+===622123242324222ma6321610.=4==216{16=3.456 1 1bd 2 168.22 1 1 113 4 11.3c2+4n= 3 + 4 =3+4=1+1=2+1=3=124m4646122424248224d216n2 1 1 281112.+1=2{ +8{ 1=+1=+1=11=022 2 4 41622a+bb+m3+44+6710===2120=113.cd11113232bamb436412++5a=++5{3=++15=4+4+15=2314.nd111142421112{316{312ca16na134143431134+484715.+=+=+2=+2===1232bmd2{461868624242423a6m3{36{69363616.4b+=4{4+=16+=4+=4+11=4363636361114+2{3{+8{17.b+2d3c+8d2322+11+233633=====242424244429 1 3{2+ 3{2{ab3{2+d2222{3{4212{14424 2 118.+a{n=+3{=+3{34344342392{123{2324239364+912615=+=+=8+===783423428288EJERCICIO13Paralosproblemas1al24lasliteralestomanlossiguientesvalores:a=1b=2c=3d=4m=1/2n=2/3p=1/4x=01.(a+b){cd=(1+2){34=3{34=94=5()()()(2.a+bba=1+221=3{1=3) 1 2 41 92 7+8()(2)3.bmcn+4a= 2 3 +4{1= 2 3 2 +4={+4=+4= 2 3 2322377=1512=724.(2m+3n)(4p+b)= 2{2+3{2 4{4+2 =(1+2)(1+4)=3{5=15 21 3 12 1 ()( 2)(4 22) 3 15.4m+8pa+b6nd= 4{+8 1+2 6{4 =2+2{3{0=022() 2 ()

9. 21 1()()()()(6.cbdcbamp=324321 =1{1{1 )()() 211 4 =4 4 12 3+4 716871612(2)2(7.bc+dam+n+2x=23+41 2 )()+ +2{0=4{7 23 6 =28=66=6=2656()1()8.2mx+6b+c4d=2{{0+62+34{4=64+94{16=6{1364=7864=142222222() 11 8{16{ 8m16p + a=2+4 {1=4+4=4+2=2+2=2+6=8=229. 9nb 3 9{22 1826333 3 3(10.x+ma+dc=0+bca)2(1+43)=2(1+643)=2{62=31123111 11 11.(4m+pa2+b2= 2)4 + 4 1+222 2+1 1+4=4 35327=4{===522ac132 4 9495559()(12.2m+3n+4p8p+6n4m9n+20p)() 11 11 21 = 2{+3{+4{ 8{+6{4{ 9{+20{ =(1+2+1)(2+42)(6+5)=4{4{11=17622 234 432 34 (13.cm+ndm+p+bn+p222)()() 1211 21 73112144126144+4426=32 + 42 + +22 + =9{16{+4{=12+===212=212 23 2434 641221212126 c2+d2 2 32+422 1 9+162 1 252 115 m= {= 2 12 {2= 12{2=5{2=2=22114. ad 14 15.(4p+2b)(18n24p)+2(8m+2)(40p+a) 1 1 1 1 = 4{+2

{2 18{24{ +2 8{+2 40{+1 =(1+4)(126)+2(4+2)(11)=5{6+2{66=30+132=1622 4 34 2 4225+25+d24 1 2+416a+5+21+ b{m=2{ 2 2{4=2{5+8=3{5+8=3{13=3{208=624=31216.=dbp2421 22121212122 4 16161616 2 2902882()2()17.a+b{c+8bm{n=1+2{3+8{2{ =3{25{=3{5=15=2212 3 12232666==144=142663 2 a+c 1+36{ 6n 1 44 (c+d){p= (3+4){3 124 ++= + 7{==18. 2 b 22 4 22 277 210.()()19.3cb{32m2da{16p2n=3(32){32{2(41){16{=3{166{4=3{46{23=12123=31126242236abc3mncdnp20.+2{8b2(ba)abc12213{{6{1{2{33{4{{=+2334=36+12=6+11=18+128=22=112{8{22(21)1{2{32{1626823242412a2+b212+225+2162212+3(a+b)(2a+3b)=2+3(1+2)(2{1+3{2)=+3{3{8=+72=5521.==732ba2212333332 11 11 11 22.b+ + + + + 2 ab bc nm 2 11 11 11 22 35 3 5 7 21497035=2+ + + + + =4+ { + +2 =4++ =+2===1721 12 23 21 26 2 4 2 4442 32 (2m+3n)(4p+2c)4m2n24189418522 12 1 1 2 = 2{+3{ 4{+2{3 4 =(1+2)(1+6)4{{=3{7=21=23.144==2095 23 4 2 3 499999c322b2223n=33=33=34=64=5428=2624.2abmbm1113797963632{1{22422222EJERCICIO141.a+b+m(10.$x+am)18.x2m22.m2+b3+x4(11.mabcKm)()(19.$3a+6b$ax+bm)12.$(n300)3.a+1a+220.(a+b)(x+y)4.x1x213.(365x)das21.$(8x+48)5.y+2y+4y+622.bs.(a8)(x+4)14.$8a$15a$ma(6.$a+x+m)c15.2a+3b+757.mn223.sucresx(8.bs.x6)16.a{bm2a(9.xmKm)17.23nm224.$m11.3.00025.n1colonesa+b29.$m2x26.a3soles x 30. x+2x+ hab.2 mm27.14 a2a 31. 1000 a++sucres34 . x+1km28.haEJERCICIO15321.m,nm+n20.4x2y,xy8()2.m,nm+n=mn34x2y+x2y=32+32xy=292xy3.3a,4b3a+4b8884.5b,6a6a+5b3321.mn,mn()5.7,67+6=76=184333636.6,96+9=3mnmn=mn=mn84887.2x,3y2x+3y22.a,b,ca+b+c8.5mn,m5mn+(m)=5mnm23.a,b,cab+c9.5a,7a5a+7a=12a24.a,b,2cab+2c()10.8x,5x8x+5x=8x5x=13x25.3m,2n,4p3m2n+4p11.11m,8m11m+8m=3m26.a2,7ab,5b2a27ab5b212.9ab,15ab9ab15ab=6ab27.x2,3xy,4y2x23xy4y213.xy,9xy9xyxy=10xy28.x3,x2y,6x3x2y+6()14.mn,11mnmn+11mn=mn11mn=10mn29.2a,b,3a2a+3ab=5ab121215.a,bab30.m,8n,4nm8n+4n=m4n232331.7a,8a,b7a+8ab=ab333316.b,cb+c123545432.x,y,x234121234617.b,bb+b=b=b132xx+y=212x+y=x+y3333324383431111218.xy,xyxyxy=xy=xy322222233.5m,m,3mn32323528219.abc,abcmmmn=mmn=mmn55535353325abcabc=abc=abc34.7a2,5ab,3b2,a25557a2a2+5ab+3b2=8a2+5ab+3b212.35.7mn2+17mn25m4m=10mn29mEJERCICIO1636.x7x8xy+4xy+5=6x4xy+53322321.3a+2bc37.5x2x2+9xy6xy+7y2=4x2+3xy+7y210.ab+bc+cd2a+3b+c8ab3bc3cd38.8a2ba2b+5ab211ab27b35a+5b5ab+2bc+2cd=9ab6ab7b2232ab2.7a4b+5c7a+4b6c39.m8mn+7mn+7mnn3222311.axayaz=mmn+7mnn3223c5ax7ay6az3.m+np4ax+9ay+8az112140.aa+b+b6mn+p2435ay+az2110+31130=a+b6=a+b641541512.5x7y+84.9x3y+54xy+641.aa3b+4b8c+8c=bxy+43x+8y+95x+4y92x+2342.m3+5m35m34m2n4m2n7mn23x=m38m2n7mn213.am+6mn4s5.a+bcam5mn+6s43.9xx11y6y+4z6z=8x17y2z2a+2b2c3am5mn2s3ab+3cam4mn44.6a+9a5ab7b8b1122222b=15a5ab15b112214.2a+3b



6.p+q+r6b4c45.xy+xy5xy+7xy4y822223342p6q+3ra+8c=2xy34y48p+5q8ra+9b+4c114r46.3aa+bb4+62215.6m3n6112514n+5p=a+b+2=ab+222227.7x4y+6zm5p10x20y8z123221555m7nx+x+xyxy+y2y25x+24y+2z47.2433662x2+322152116.2a+3b=x+xy=x+xy4343+5c48.2m+3n68a+648.5ax5ax6ax+1+ax+1+5ax+1+8ax+2=8ax+23m8n+8+7c93222115m+n1010a+3b+12c749.x+xxyxy+y2+5y243334m4n83+4231+1527216217.2x3y=xxy+y=xxy+y43343+5z+99.5a2b3c6x432111550.aba2b+a2b+ab2+ab2ab27a3b+5c3y54422631+423+353218a+5b3c8x+5z=ab+ab=ab+ab2246266ac13.18.8a+3bc21.5ax3am7an24.a+bc+d5ab+c8a+5a9axmnab+cdabc2a+3b2c+d11ax+5am+16an7ab+4c3a3b+4cd14ax+7am19a+3c3a+2ca+122.6m7ma+25ma+325.5ab3bc+4cd19.7x+2y4a+1a+2a+3+2bc+2cd3de+9y6z+54m7mm2ab+4bc+3dey+3z65ma+1+3ma+2+12ma+3ab3bc6cd8x3y55ma+111ma+2+6ma+32ab15x+7y3z1026.abbc20.mnp23.8x+y+z+uc+dm+2n5c3x4y2z+3ua6m+3p+4cd4x+5y+3z4u5m+2n8a+d9xy+z+2uadm+3n+2p9y+3z+2u2aEJERCICIO177.m2+n212.a34a+5+4n23mna32a2+61.x+4x2x25x5m5n22+a7a+422x2x4m23mn2aa211a+1532.a+ab28.3x+x313.x2+x62ab+b24x2+5x7x23+5aab+b22x+4x632x3+8x53x18x+9x623.x3+2xx2+49.x23xy+y214.a3b3xx+2x+432x+3xy2y22+5ab4ab22x2+3xyy2a37ab2b34.a43a2x+3xy2y222a3+5a2b11ab22b3+a3+4aa4+a33a2+4a10.a23ab+b215.x3+xy2+y3+a5abb22x5xy32y35.x2+3x2a+8abb222x34xy25y3x3+6b24x35x2y3xy25y3x3x2+3x+611.7x2+5x67m2n+4n36.x24x16.4x+8x92+m3+6mnn327x+6x27x+14m+7mn32+5n33x254x2+6x1+6mn2+8n34x211x+114.24.8a2m+6am2m317.x4x2+x+a35am2+m3+x34x2+54a+4am3am232+7x24x+6+7a2m4am26x4+x3+2x23x+113a+3am6am322618.+a+a4+6625.x5x3y2xy4+a53a3+8+2xy4+3xy23y5+a3a214+3xy324xyy54+a+a+a2aa65432x5+5xy4+2y52x5+2x4y+2x3y2+3x2y319.x5+x9+3x47x2+626.a5+a6+a23x34x+5+a4+a3+6x5+3x43x37x23x+2+3a28+5aa54a2+65a20.a+a+a+a+a+43643+a2+527.a4b4+4a+7a2a3b+a2b2ab38a263a+5a3b4a2b24a3+5a14a3b+3a2b23b42a4ab34b421.x4x2y25x3y+6xy328.m3n3+6m2n4xy3+y4+n34m2n+5mn24xy226mn33+6mn2x45x3y5x2y2+2xy3+y462m+n2mn33211mn222.+x+xy229.ax3ax2x2+4xy7y2x1+5a+6ax3x2+6xy+5y2+7ax3+ax46x24xy+y2+ax113ax37x2+7xyy2x1x2a+6ax3a+ax423.a38ax2+x330.ax+ax+1+ax+26axx+5ax2323ax+3ax1+ax23a3x35a2xax+4ax+35ax+2a+14axx323+ax1ax2+ax+25a32x32ax+ax+1+ax+33ax+2x+3x+2x+1 a3a+a2ax15.52223EJERCICIO186.xy+xy6341211.x+xy1x2+12y1xy2368211+xy+y21x2+12y+5xy24346122+31151512216+3+6296+10x+xy+y2=x2+xy+y2x+y+xy2642646241227213113721=x2y+xy x2+xyy2.a+2ab26241231224112127.a3ab+b3ab+b242325211ab2b3+ababb28645133312abab21152232452a+2ab+b=a2+b410104+1343251033532a+ab+b+ab4856578251782=a3ab2b3+a2b a3+a2bab2b33.x2+xy48564385318.x4x2+5xy+y262333+xx5238xy+y26334533x+xx4153+22564x2+xy+y6353424+5336xx+2+x+x2515568=x2xy+y2=x2xy+y26333299239=x4x2+2+x3x x4+x3x2x+25685283212231234.xy9.mmn2+n4234521213312xy+y+mn2n+mn5685612112m3n3mn+xy+y21032+332+122353132324+13+1+22323m+mn+n+mnx+xy+y=xxy3856410641051625116=m3mn2n3m2n m3m2nmn2n33856338522112245.a+abb10.x4+2x2y2+y352752112543221413aab+bx+xyyxy610668146122145312112xy+yxya+abb4761220365416+322241+2413538+101242+13+122x+xy+yxyxya+ab+b6814661220611722541353=x4+xy+yxyxy1723417232681466=a+abb2=a+abb21220612203145317221354 xxy+xyxy+y66861416.23411.x+13.a+65xxa4a23535331132+aaa3x5x+x5821083452131224aa+6+xxx786433133a6x+x481257348523533438+21381+632224a6+a+a+aa+a2x5+x+x+xx4785881210831043235337=a6a+a+aaa78588731312=2x5x+x+x2x443510433327121083 a6+aaa+aa578882731213 2x5x4x+x+x431281023521314.x5y512.a+axx1323415963+xyxyy104637213a2xaxx15y+345xyx2y3789956232152112xyy+2x4ya3+a2xax533241432341832653+1045x5+xyxy+y+xyx2y32636+722021623131041856a+ax+ax+x332342951345914249=x5xyxyy+xyx2y3104185641274=a3+axax2x3 x5+134xy33252334295xyxyxyy9142495106418EJERCICIO19Paralosproblemas1al14lasliteralestomanlossiguientesvalores:a=2b=3c=10x=5y=4m=2/3n=1/53.x4y41.4x5y2x45x2y283x+6y84x4+7x3y+10xy3x+yx4y45x2y28+7x3y+10xy32y8 x4+7x3y5x2y2+10xy3y48 2{48=88=0=54+7{53{45{52{42+10{5{43448=625+28{1255{25{16+50{642568=625+3.5002.000+3.2002568=3.8112.x25x+8x2+10x304.3m5n+66x2+5x506m20n+86x2+10x7212m20n12 6{52+10{572=6{25+50729m45n+2=150+5072=172211845 9{45{+2=+2=69+2=1353517.5.nx+cnab8nx2cnab10.x3yxy3+5nxab55x3y6+x4x2y210nxcn3ab56xy+23+x2y211 10{{510{3{2{35+3xy3+1y4556x3y4xy3+2+x4y45010=6{35 x+6xy4xyy+2433455=102185=15=54+6{53{44{5{4344+2=625+24{12520{64256+26.a3+b3=625+3.0001280256+2=2.091.3ab+8abb3225a36ab2+832a22b+11.+3ab22b343114a3+2ab2b3+82ab+b239 4{2+2{2{32{3+832311+abb2=4{8+4{92{27+863=32+3654+8=42322+16+132aab+b4697.27m3+125n3314=a2ab+b29mn+25mn2246914mn28314 {22{2{3+{32+10mn+11mn2246931427m3+m2n+22mn2+125n38={4{6+{9=31+4=63223469 2 2 12 1 1 27{ + {+22{{ +125{ 8 3 3 53 5 5 9225218414411m+n=27{+{+{+125{812.17344279532512572521444444m+n+15mn=8+++18=++1341724575457572120+132+225377m30mn===1152225344225225+3a1+yb2+mx418+77225+1021+21+128.xm+n+45mna1b2x4343442x2y2m18235212b2=m+n+45mn+3y2mx434344923523xa1+2yb23mx4 17m45mn+34n+354 2 229 2 2135 1 3{521+2{4323 =15+82=21= 45{{+17 3 +33534 5 3 9490351={+{+3b1x31791534259.nm+843547=6++3=+35nb13mx3+1017



8501717040+75104634nb1+5mx318===2123170170170mx353 2 2 24 = = 3 3 918.12313.bmcn214.0,2a3+0,4ab20,5a2b25321+0,6ab20,3a2b0,8b3bmcn+64100,4a30,8a2b+6121bm+cn+40,2a3+15a2b+0,9b3,4251b2m+2cn+3ab20,1a2b+0,1b3+685 0,1ab+ab+0,1b3+6224+6212305+2+10010+30+20+3bm+cn+=0,1{22{3+2{32+0,1{33+6850572674372267143=0,3{4+2{9+0,1{27+6 bm+cn+={3{+{10{+8505835055=12+18+2,7+6,7{9{2674312667043216743=++=++=++=25,5245052425054255525+268+8601.653===1610053100100EJERCICIO2021.8xa+211=8xa+2111.85=1322.6an(5an)=6an+5an=11an2.74=113.811=323.45ax1(60a)=45a+60a=15ax1x1x1x14.8(11)=8+11=324.54bn1(86b)=54b+86b=140bn1n1n1n1()5.19=1+9=86.2a3b=2a3b25.35ma(60m)=35m+60m=25maaaa7.3b2=3b2 1 110+111126.5 =5+= 2 ==528.4x6b=4x6b2229.5a6b=5a6b23891727.==()10.8x3=8x+334121211.9a5b2=9a25b2212 22 122232228.x x =x+x=x=x3 3 333()12.7xy5yz=7xy+5yz43 53 24+25349313.3a4a=a29.xy xy =xy=xy5 6 303014.11225m2=14m2m12 32 1+62526x2y(x2y)=6x2y+x2y=5x2y30.ab ab =ab=ab15.8 4 8816.11a3m2(7a3m2)=11a3m2+7a3m2=18a3m231.23=5()32.71=7+1=817.8ab2(8ab2)=8ab2+8ab2=033.8(5)=8+5=318.31x2y(46x2y)=31x2y+46x2y=77x2y34.5(4)=5+4=919.84a2b(84a2b)=84a2b+84a2b=035.7(7)=7+7=020.3ax+15bx+2=3ax+15bx+236.2a(5)=2a+519.37.3xb=3xbEJERCICIO2138.2n5m=2n5m1.a+b2.2x3y(39.3b6a=6a+3b)a+bx2y40.8b(5a)=5a+8b332b3x5y41.7a(9)=7a+93.8a+b4.x3x2(42.25ab25=25ab+25)3a45x611a+b4x2+2x6()43.3aa=3a+a=4a44.4b(3b)=4b+3b=b5.aab326.xy+z54x3(11x3)=54x3+11x3=65x37a2b9ab2x+yz45.a38a2b9ab2046.78a2b14a2b=64a2b47.54a2y(43a2y)=54a2y+43a2y=11a2y48.ab9ab=10ab7.x+yz8.x2+y23xyx+yz3x2+y2+4xy49.31xy(31xy)=31xy+31xy=022222x+2y2z2x2+2y2+xy50.3aa=4axxx 2x2+xy+2y251.311ax+1(7ax+1)=311ax+1+7ax+1=318ax+19.x3x2+610.y2+6y3852.105m9m=96mxxx5x6+4x23y2y246y53.31ax118ax1=49ax1x6x23+4x4y22y4+6y36y8 2y4+6y3+4y26y854.236ma(19m)=236maa+19ma=217ma55.85ax+254ax+2=139ax+211.a36ab2+9a+8a15a2b556.(6a)=+6a1144a36ab2+17a15a2b522+1513 a315a2b6ab2+17a557.(5)==33312.x4+9xy311y4733358.mm20y4+8x3y+6x2y210856303863433x4+9xy331y4+8x3y+6x2y2=m=m=m808040 x4+8x3y+6x2y2+9xy331y4522 1122 13.a+b+cdab+2ac3cd5de59.ab ab 14.6 12 8ab+4ac+5cd5dea+bc+d10+11222122722=ab=ab=ab2a+2b7ab+6ac+2cd10de1212415.x3+6x29x1913260.ab45a3b26x3+11x221x+439140532406325x3+17x230x+24=ab=ab=459a3b219920.16.y9y+6y3153231y3+8y2+11y4+19yy540y3+14y2+11y4+19y31 y5+11y440y3+14y2+19y3117.5m39n3+6m2n8mn25m3+21m2n14mn2+189n3+27m2n22mn2+18 27m2n22mn29n3+1818.4x3y19xy3+y46x2y225x3y+51xy332x2y2+x429x3y+32xy3+y438x2y2+x4 x4+29x3y38x2y2+32xy3+y419.m+mn9mn+1964224+30m2n4+61+13m3n316mn5m6+m4n2+212n4+80+13m3n316mn5 m6+m4n2+13m3n3+21m2n416mn5+80m20.a5b+6a3b318ab5+428a6+11ab42+11ab249b68a6a5b+11a4b2+6a3b3+11a2b418ab59b6+4221.1x+xx+3x6x243524+30x28x415x+x625+29x27x4x312x6x5+x6 x66x57x4x3+29x212x+2522.6x2y3+8x523x4y+80x3y218+51x4y+21x3y280+y59xy46x2y3+8x5+28x4y+101x3y298+y59xy4 8x5+28x4y+101x3y26x2y39xy4+y59823.m68m4n2+21m2n46mn5+823mn514mn33+24mn58n6+14m6+23m5n8m4n214m3n3+212n4+18mn58n6+22m24.x8x+16x23x1575251x+18+8x625x4+30x3x759x+16x523x2+3+8x625x4+30x3 x7+8x6+16x525x4+30x323x259x+325.9a615a4b2+31a2b4b6+14+15ab423b25ab53ab+9ab653359a6+31ab4b625a5b53a3b3+9ab5+14 9a625a5b53a3b3+31a2b4+9ab54b6+1424ax+ax+1ax+25ax+6ax+1+ax+226.4ax+7ax+121.a127.mma+3ma24ma5ma23ma+18ma35mama12ma23ma+18ma3 3ma+1+5mama12ma28ma3m+428.a7am+28am+6am1+14am+2+8am1+5am+3+11am+1am+4+7am+28am+14am1+5am+3+11am+1 am+4+5am+3+7am+2+11am+18am+14am1a+229.x7xa+9xa1+25xa219xa45xa1+11xa+160xa3a+2a1a2x26x36xa+25x+11xa+160xa3 xa+2+11xa+126xa36xa1+25xa260xa3n+1n230.m6m+8mn319mn55mn26mn39mn58mnmn4mn+111mn2+2mn328mn58mnmn4 mn+18mn11mn2+2mn3mn428mn5EJERCICIO22ba7.a+2b3cbaa+b2c1.2b2a 2a+2b2a+3b5c2.2x+3y8.3n+4m+5px+y+nmpx+4y2n+3m+4p 3m2n+4p3.7a+59.x+3y6z5abxy+z2a+5b 2ab+52x+2y5z4.x2+610.5b2+8ab+a2x2+5x6b2ab3a22x+6+5x 2x+5x+622b2+7ab2a2 2a2+7ab+b25.x2y+5xy25m2n2+6mn+xy2x3m2+n2+3mn11.x2y+6xy2x3 x3+x2y+6xy26m2+9mn6.7a2b+5ab212.8x2+5x46a2b+8a3+x6+x3ab+5ab+8a 8a+ab+5ab2233228x2+6x10+x3 x38x2+6x1022.14m28n+1623.y+y+y+963213.14m29m323y3+58y4+15y5+8y8n+7m3 m38n+7y622y3+y2+148y4+15y5+8y y6+15y58y422y3+y2+8y+1414.8ab+5bc+6cdab+bc6cd24.xx+3x5x986427ab+6bc367x75x5+23x351x15.a9abb323x8x6+3x45x2457x75x5+23x351x25a2b+b3+8ab2 x87x7x65x5+3x4+23x35x251x45a334a2b+8ab225.x73x5y2+35x4y38x2y5+6016.6x8xy6xy322+60x4y3+x2y5y790x3y4+50xy6xy2+6y34x3xy+95xy7xy+60y790x3y4+50xy67524325 x73x5y2+95x4y390x3y47x2y5+50xy6y7+606x38x2y7xy2+6y34x+317.m29n+11c+1426.a8ax+15m27n+8cd+5ax+1ax+2+6ax16n+19c+14d 19cd16n+14ax+33ax+15ax+2+6ax ax+3ax+23ax+1+6ax518.5a+9ab40ab3+6b4437a3b+8a2b25ab3b427.8an+16an4+15an2+an35a4+2a3b+8a2b245ab3+5b47an5an2an38an115an+16an4+10an28an119.x58x4+25x2+15n1n2 15a8an+10a+16an46x2+76x3+9xx58x4+19x2+226x3+9x28.15xa++5xa+6xa+41xa321 x58x46x3+19x2+9x+22+9xa+2+18xa131xa+1+xa+420.3xy48x3y219y5+1815xa+3+14xa+26xa+59xa131xa+1+xa+46xy4



25y5x+xy523 xa+4+15xa+3+14xa+231xa+16xa+59xa19xy48x3y244y5+18x5+x2y3 x58x3y2+x2y39xy444y5+18m129.9a21am2+26m3+14am55am112am2+am+8am421.x36x4+8x29+15x25x3+18x2+4625x+11x514am133am2+26m3+14am5+am+8am4 am+14am133am2+26m3+8am4+14am524x36x4+26x2+3710x+11x5 11x56x424x3+26x210x+3730.15mx+3+50mx+114mx6mx1+8mx222.a526a3b2+8ab4b5+6mx+4+23mx+2+6mx+1+mx18a4ba3b2+15a2b3+45ab4+8mx+415mx+3+23mx+2+56mx+114m5mx1+8mx2xa8ab27ab+15ab+53abb+145432234523.EJERCICIO2311.x12xyy21.1a+1x21xyy2 x2xyy21a+212.a3+62.05a2b+8ab2b3a+8a35a2b+8ab2b3+6a+813.x3+y39+5xy17xy22+53.3aa+52x+5xy17xy+y+532233aa4 a3a42214.x414.+169xy+8xy+15xy32235xy+x162x9x3y+8x2y2+15xy3145xy+x2 x25xy15.a5+b5+11ab2ab8ab+4ab4233245.1a+11a4b2a2b38a3b2+4ab4+b55a3+a2bab2 a5+11a4b8a3b22a2b3+4ab4+b51a+abab a+abab+132232216.x4+x2+506.x35x3+25xx3+8x2y+6xy2x45x3+x2+25x+502x3+8x2y+6xy217.y+y41637.a9y517y4+y318y2+8a2b6ab2+b3y6+y419y517y4+y318y2a3+8a2b6ab2+b3 y69y517y4+y318y2+y418.+y418.a6+9a4b2+a2b45x3y7x2y2+8xy3+15ab517ab33+14ab5+b65x3y7x2y2+8xy3+y4a6+15a5b+9a4b217a3b3+a2b4+14ab5+b619.x+x11x439.m45m4+18am37a2m2a3m+a45x+x2+344m4+18am37a2m2a3m+a4x4+x316x+x2+34 x4+x3+x216x+3420.m3110.16m2n7mn2+3n314b+acdm3m2n7mn2+3n3130b+acd abcd+3024.EJERCICIO2453231.12a6.6m+9n2121213123a+abb2+n+mnmn24355282+12125310+93123a+abb2m+n+mnmn24356452832122=a+abb513193435 m3+m2nmn2+n628452.1532134257.a+abb2xyyz+7355395211aab+42135+51428xyyz+5396522342140a+ab=xyyz+1465391213142aabb2+=xyyz+155914658533251238.x+xyybc86103.5323132x+xy2y2bc+ab+cd51064915+24250+181+20218532x+xyybc+ab+cd406010304939268212392172123132=x+xyy=x+xyy ab+bc+cd406010401510430959.a+a+3212a4.ab6237297421+aaab+81085928+7210+92021586+21a3+aa+ab+810241092152191381=a+3aa=ab+81024109274310.m+12mn32n523275.9x8y55211253mn2n3+mn+yxy+92181071121204+735215230+825xyxy+3m3+mn2n+mn+98071136721853825351111=x2yxy+m3+m2n+mn2n3+980711213678551923 x2xyy+97401125.3435324137811.x+x3yxy+y12.a+bc+d547325895221547117x4xy+xy3y+bc+d836208983543351573454112+77+18+17x+xyx2y2xy+ya+bc+d5482162208982358314119897=x4+x3yx2y2xyy=a+bc+d5482162208981197=a+bc+d2208EJERCICIO251.3256.52121aaab+ab8684357253a2+ab6a686920251125522+721+1853aa=aaab+aba246246883652921953=ab+aba2.8a+6b588361355919a+b a3+a2b+ab225688316130+31533a+b5=a+b525252352217.mn+mn+mn3622111433.x+xy6337222m4mn+mn37289xy9232049223+2m4+mn+mn+mn36672111569x3+xy6=x3x2y699229225=m4+m3nmn+mn36115694.a+bc132a+bc2437413222314214+33+21758.xy+xy+xy+xy7a+bc=a+bc814332432431533212xxy+xy427892515.m+n+p157416322238+3463+2362xxy+xy+xy+xy28143249mn+p15745322231146523561+2113=xxyxy+xy+xym+n+p=mn+p281432493623621574532223114=xxyxy+xy+xy729281432426.752421269.xy+xyx3y3x2y4+xy5+y93813742124x6+xyxyxy5+y6911756+74213311+1242+136713421331224156x6+xy+xyxyxy+y=x6+x5y+xyxyxy+y9981113998111313725273210.xxy+xyy39811523123x+xyxy263641+231432562732+301121732xxy+xyy=x3xyxy2y331881151881153423245611.mnmn+n107926742524163m+mnmnn+13201435266+7426+52453632613421124263m+mnmn+n+=m+mnmn+n+132014951320149535747321231512.8c+22cd+12cd+cd23d3554532335+cd+cdcd4d116413357+1047+10321233413+95c+cd+cd+cdcdd358221224393174173212334225=c5+cd+cd+cdcdd35822122439EJERCICIO26Paralosproblemas1al14lasliteralestomanlossiguientesvalores:a=1b=2c=3x=4y=5m=3/2n=2/52.a+b331.aab2+2b3+5a2b6ab23abb2a+3b3+5a2b6ab2 a3+5a2b6ab2+3b33a24abb2=13+5{12{26{1{22+3{23=1+5{26{4+3{8=124{1{222=184=11=1+1024+24=1127.13.a22318.3mn+4mn2n22315ab+c231212131215115mn+mn+n+m3ab+c=ab+c6422232234+123+1251151mn+mn+m3=m3+m2n+mn2 {1{2+{3=1+56462232322 3 5 3 23 2 275183412+107= + {+ =+{+{===321 2 6 2 52 5 86202252227312675+150+48873=++==84502002004.3m5n22m210n28mn9.a53a2b4+b52m215n28mn 2m28mn15n222ab+5ab4233 3 32 2 9484=2 8{{15 =2{3{aa4b2+5a3b33a2b4+b55 2 25 5 41059241245482427=1514{22+5{13{233{1224+25=====14+5{83{16+32=14+4048+32=2125510105.x418x2y2+15y410.ab+10mn8mx16xy3+6xy9y4315abx4+16x3y18x2y2+6xy3+6y416ab+10mn8mx323=4+16{4{518{4{5+6{4{5+6{5432234=16{1{2+10{{8{{4252=256+80{6418{16{25+24{125+6{625=32+648=74=256+5.1207.200+3.000+3.750=4.926311.a6.a7am+m323+5am+5m38a2m211a2b+9ab2b3a32am2+6m38a2m a38a2m2am2+6m3a311a2b+9ab2b33 3 2 3 243927=1311{12{2+9{1{2223=138{12{2{1 +6 =12{+6{22 2 248=122+368=798144818+8119=112+==24441412.x64227122537.a+abb2xx+385368112142253a2ab+bxxx+61064368412782121211142253a+abb=aabb2={4{4{4+68102810643681112124322039625680+9 {12{1{2{2==4+=28102810368241121058323177======985245202024828.322213.x3+xyxy2x1x516514.a+aax3+ax233321356x+xy+y4525ax1+9ax3ax2433322321325x1x554x3x+xyxy+ya+aa416525561321213349x3 x3+xy+xy+y axax1+a4165255613211334943={43+{4{5+{4{52+{5=14{141+{1416525561154125349+3018+245257={64+{16+{25+=1+===81730416525563030=16+15+20+5=56EJERCICIO277.m+npmn+p1.+ab+b2a22m2n+2pm+npa25b2
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a2ab+4b2mn+p0a2+ab4b2ab+4b28.9axa2x25ax+3a22.a+819ax+7a2+25x225x26a2a+6146a2+25x224x25ax3a214139.5a2+6a4a313.x+4xy28a+62a35a2+2a232a3+5x2y+y32a3+5a22a+2a35a2+2a3x3+5x2y+4xy2+y35x39x2+4x417xy211x7x436x11x4+2x3+9x2+6x410.x35x2y4xy2y311x42x39x26x+412x4+2x3+9x2+6x5x312x2y4xy2y311.35a2b7ab211a3+b37a35ab+8ab+63227aab32+54.3mn+4mnn3235m47a3+ab528aab+b+53233mn4mn+5n3324n3+4n35m44n312.11n4+14n225n+85.8a+9b3c6a19n36n2+9n47a9b+3ca11n4+19n3+8n216n+4a5an57n3+4n6.ab+ca+bc11n19n38n2+16n442a+bcaa2a+bcn5+11n426n38n2+20n429.20.x46x2y2+y4x42x2y2+32y413.6a3m+5am36+8xy+31y224x42x2y232y47a5am11am43226m4x4+2x2y2+32y407a11am11am+5am6m643223421.6n+n+n254a48a2m2+m4+7n3n28n67a4+11a3m+11a2m25am3+6m4+66n5+n4+7n38n66a4+11a3m+3a2m25am3+7m4+66n5+n4+7n38n64x4y+13x2y39xy4n6+3n4+8n31914.6x5+8xy32+xy42y5n6n+4n+15n8n2565436x4xy+8xy+13xy8xy2y5432234522.a53a3b2+6ab4x530x3y2+40xy4+y5+22ab+10a3b211ab4b546x5+4x4y8x3y213x2y3+8xy4+2y5a5+22a4b+7a3b25ab4b57x5+4x4y38x3y213x2y3+48xy4+3y5a5+22a4b+7a3b25ab4b515.a+b2a5ab4+7ab23b5ab2a+ba5+17a4b+7a3b2+7a2b35ab42b52ab16.8x+98x+6y+46y5223.4m35m22m3m35m2+6m+48x+6y+48x+6y+67m3+8m+4m4517.x26y2x7xy+34y223m5m+6m+432m3m5m+6m14327xy+40y29y21624.7a211ab+b22b28x27xy+34y2x27xy+43y2167a2+11ab+b28+418.4a+8ab5b225a+ab+b222b282b24a27ab+6b24a2ab+b225.3a4b+5c5a2+ab+b2a2+2b27a+8b115a+6b2c11a+2b7ca+b+2c19.x3y35a+6b2c116a+7b1114xy+5xy22x14x2y+5xy2y3326.5a3+14a219a+8a5+9a1x14xy+5xyy3223a4+3a213x319y3aa54+5a+17a10a+6324x314x2y+5xy220y3a4+3a35a2a+8a+17a10a+1543230.27.m4+10m2n2+15n45+y529.x11mn14mn3mn+n432233xy+21xy+18xyy543223m11mn4mn43223mn+16n34x5+3x4y+21x3y2+18x2y36m4+7m2n2+8mn3n4x5+32x4y26x3y2+18x2y32xy4+y5m+11mn+4m2n2+3mn316n443x53x4y21x3y218x2y35m+11mn+11n+11mn17n4m3223429x4y47x3y22xy4+y528.a5+4a3b2+8ab4b5x130.3a+6ax7ab4+15ab25ab+3b2345ax7ax1+ax2a3b2+3a2b35ab44axax1+ax2a57a4b+3a3b2+18a2b322ab4+2b58ax+27ax+1ax+12ax13a56ab21ab23464ax+ax1ax2a+7ab3ab18ab+22ab2b543223458ax+27ax+15ax+13ax1ax22a+7ab3ab24ab+ab54322342b65EJERCICIO281.x2+5x4x2+2x16.a2x3x35a2x+11ax211x32x6x+62a3+3ax2a4a2x+6ax2+8x33x+2x122x+2x32a3+a2x+3ax23x3a39a2x+17ax23x32.3a5b+c7a+b4a6b2cab3c8b3c7a+7b+3ca3+a2x+3ax23x3a3+9a2x17ax2+3x34a6b2c7a7b3c3a+b+c10a2x14ax23.x3+19x+46x3x2+85x3x2+73x2x+13x28x56xx+8323x+8x+526x+2x28x+337.x4+x23a+12a4+2a+a32x33x+57x3+8x23x+44.a31a2a4ax45x+4x2x43a3+a2a4+aa4+a3+a2a2xx4x+x+2432x7x+8x3x+14325.ab+bc+ac5ab3bc+4acab6bc+9ac92x4x34x2+x+27bc+8ac9ab+3bc+5ac4ab9acx4+7x38x2+3x1ab6bc+9ac94ab+9ac3ab6bc9x4+6x312x2+4x+131.8.m4n417mn4mn7mn3322m4+617m3n+2m2n27mn381n4m4+6m2n280n4m2n2+mn34m4+m2n2mn3217m3n+2m2n27mn381n4m4m2n2+mn3+2m4+17m3n+3m2n28mn381n429.+a3+a7aa546a2+8a44a3+a2a5a4+a311a210a+275a211a+2616a38a27a15+a412a3+7a2+7a+15a5a4+a311a210a+27a4+12a37a27a15a511a34a23a+4210.3x2y2x23xyy220x211xy+8y211xy+9y14219x8xy+9y223x2+11xy8y2+143x211xy+8y21420x211xy+8y217x2+1411.a1a2312.a2ab+b2a+1a43a28ab+7b2a2+9ab+3b2a2+ab4b203a+85a+11ab17b228ab7b2a22ab+9b2a22a+1a2+2ab9b2a2+ab4b2ab+5b213.m41m3+8m26m+5m516m516m4+7m219m7m+1216m+7m342m+m7m2+13m543m4m3+7m213m+5m516m4+7m219m517m4+m3+13m2414.x5y52xy+5xy7xy432233y57x4yx3y2+11xy4x5+2x4y+2x3y2+7x2y36xy4+4y5+87xy32+6xy48xy417x4yx3y2+10xy41x2xy2xy7xy+6xy4y8543223457xyxy+10xy14324x+9xy+xy+7xy+4xy4+4y5+754322315.a+7a48a63a5+11a3a2+46a411a32a+83a4+7a28a+55a53a47a3+48a258a+135a3+5a4a+125a57a+41a50a+832a+3a5a4+5a34a2+14a136a63a5+a45a3+4a214a+135a53a47a3+48a258a+13a6+8a54a42a3+44a244a16.a57a3x2+9+18a3x24x5820ax4+21ax19ax2349ax17ax+11ax43223+9a3x27ax4+x580a5+36a20ax+2ax+21ax26ax+x7154322345a9ax+ax5432+11ax4x235+28a59a4x+a3x2+11a2x34x5+28a+20a4x2a3x221a2x3+26ax4x5+71511a4xa3x210a2x3+26ax45x5+9932.EJERCICIO29774325.12a4aa3+a261312751.a+ba3322341124a+a6aa+231575453a+bab7433227+94332211813434aa+a6aa+aa1275127553322+3945a+bab443322=aa+a1a1734124375531555=a+b=ab34124121526.x+yzy23495313321215132.a6a+ayz+3xy+z38259529205353323a3+a2aaa+61615+81132+1565658x+yz+3x+z5333+53329202205a3+a2+a6aa+615131131765868=x+yz+3=x+z4329202205=a3a+638373233.a+3ba+b+67.ab+ab2b35324221112523ab+6a+babab2+b535686352923114+112129102323a+b+6a+b+6ab+abb5356812337251111=a+b+6=a+b+6=a2bab2b3535281231313ab23133214.3x7x+5112ab+11ab2+b38123122xx+6131121149a+ab+ab228121361221+30xxx+314951352231=xxx+1221113314958.abb+ca+bc293529513511153xbcbcbc63591091013522311233652116+1x+x+xabcb+cac314952959102105+235221131117x+x+x31=a+bc=b+c=ac6149529591021073522=x+x+x651614933.13121122113192219.3a+8a+54a3a+43a40a3a+8331132921119231a2aaaa3+a+a54103408340410135242321131029222189108a+aa+a+aa+a+340410340381280131923113192211211=aaa+=aaa+=a+=a+34041034038128012403252222122327132110.5x6xy+9y9x+9xy3y5x+xy+36y+23111722232132711xyy2+xxyyxxyy2+2344592253943210+18232110+1721224+92139222+1xxy+y+x+xyyy+512944596218432281212722113213723=xxyy+=xxyy=y+51294459621843271213271321=xxyy+=xxyy5394536221312121323373ab+ab+ab2b311.7a5b24ab54821033135123123313a2b+ab2+ba2b+abb3a3+a2bab2+b4810482274810233232132522+12332+52315137aab+ab2bab+abbab74810482107101023323213323233723143723737=aab+abb=ab+abb=ab=ab7481048210710107510122112.mnmn3n43424322254542m+m3nmn+nmn47553145147312224541311221mmn+mnnmmnmn+mn31420431446044+1412732024+1522135+2413112212m+mn+mnmn3nmnmn+mn3n414206043460455453112210=m+mn+mnmn3n414206043541311221=m+mn+mnmn314460434.1113.x+y2331yz4621z+m5541131137113m+n+xyz+mn2382123043814+95121213113711403x+yz+m+n+xyz+mn+2123043821230438113711311371137=x+y+zm+n+=xyz+mn+21230438212304385413314.a+aa625223aa+53834331221141312152aa+aaaa+8463241223313393133+a+a+a4+a64011128209469+2341224+153916522+9112441121699.a+aaa+aa2+2412640



33242264114133201521141312152.134121117=aaaa+=aaa+=aa+2412640332412233242264EJERCICIO301.x3x2+54.x34x2+87.5a+8abb11323x+x+3x5632x3+4x2+x13a3+b33x6x54a3+8ab211Rta.x+x+3x1132Rta.x4xx+1332Rta.5a+8abb31132112.5a+9b6c5.m43mn3+6n48.xy4235a9b+6c+8x+9m4+4m2n2+3mn36n4811x+y8x+94m2n2823Rta.5a9b+6c+8x+9Rta.m4m2n23mn3+6n4+844113.a3b36.4x+5x5x232Rta.xy423a38a2b+5ab23b35x24x+88a2b+5ab24b34x39x+6Rta.a8ab+5ab3b3223Rta.4x3+5x25x235.9.5x27xy8y210.n311.05x+7xy+8y+1229m+8mn5mn+n3223a+5a8319m+8mn5mn+2n3223a3+5a8Rta.5x+7xy+8y+12210m8mn+5mn2n3223Rta.0m3Rta.10m38m2n+5mn22n3EJERCICIO311.x(xy)6.a+(ab)+(a+b)11.x+y+(xy+z)(x+yz)=xx+y=a+aba+b=x+y+xy+zxy+z=y=2aa=a=xy+2z(2.x+3xx+522)7.a+b+2aab2222212.a(b+a)+(a+b)(a+2b)=x3xx+522=ab+2aa+b22222=abaa+b+a2b=3x+5=3aa=2a222=2b3.a+b(2a+3)8.2a{x+a1}{a+x3}()(13.x2y2+xy+2x2+3xyy2+xy)[]=a+b+2a3=2a+xa+1ax+3=x+y+xy2x+3xy+yxy2222=3a+b3=1+3=4=3x2+3xy+2y24.4m(2mn)222(9.x+yx+2xy+y+x+y222)[]2[22]{14.8x+2xy+yx+xy3yx3xy22}()=4m+2m+n=x+yx2xyyx+y222222=8x2xy+y+xxy+3yx+3xy22222=6m+n=x2xy+y22=8x2+4y25.2x+3y(4x+3y)10.(5m+6)+(m+5)615.(a+b)+(ab)(b+a)+(3a+b)=2x+3y4x3y=5m+6m+56=abab+ba+3a+b=2x=6m+5=0EJERCICIO32[1.2a+a(a+b)][2.3xx+y(2x+y)][3.2m(mn)(m+n)][=2a+aab][=3xx+y2xy][=2mmnmn]=2a+aab=3xxy+2x+y=2mm+n+m+n=2ab=4x=2m+2n36.[()(4.4x+xxy+3y+2xy3x+y22222)()][11.(a+b)+(a+b)(2a+3b)+(b+ab)][=4x+x+xy3y+2xy+3xy22222][=ab+ab+2a3bb+ab]=abab+2a3bb+ab=4x2x2+xy3y2+2xy+3x2y2=3a7b=6x2+3xy4y25.a+{(2a+b)(a+bc)+a}{[12.7mm+3n5n3+m222()()]}(2n+3)=a+{2a+b+ab+c+a}{[=7m2m2+3n5+n+3m2]}2n3=7m{m3n+5n3+m}2n3=a2a+b+ab+c+a222=a+c=7m2+m2+3n5+n+3m22n3[6.4m2m+(n3)+4n(2m+1)][]=7m2+2n5[=4m2m+n3+4n2m1][]=4m2mn+34n2m1{[13.2a(4a+b)4a+(ba)(b+a)]}=5n+2{[=2a+4ab4a+ba+ba]}=6ab{4ab+ab+a}[(7.2x+5x2y+{x+y})]=6ab4a+ba+ba[=2x+5x(2yx+y)]=b[=2x+5x+2y+xy]=2x5x+2y+xy=2x+y([{14.3x5y+2x+y(6+x)(x+y)}])([=3x5y+2x+{y6x}+xy]){[8.x7xy+y+x+3xy2y22(22)]}=3x(5y+[2x+y6x+xy])=3x(5y2x+y6x+xy){[=x27xy+y2x2+3xy2y2]}=3x5y+2xy+6+xx+y=x2{7xyy2x2+3xy2y2}=5x5y+6=x2+7xy+y2+x23xy+2y2=2x2+4xy+3y2[{15.6c(2a+c)+(a+c)2a(a+c)+2c}][=6c2ac+{ac2aac}+2c][{9.(a+b)+3a+b2a+b(ab)+2a}][=6c2acac2aac+2c][=ab+a+b{2a+ba+b}]=6c+2a+c+a+c+2a+a+c2c[=ab+a+b+2ab+ab]=6a+7c=aba+b+2ab+ab=a2b()[{16.3m+n2m+m+2m2n5())}(n+6)](=3mn[2m+{m+(2m2n+5)}n6]{10.(x+y)4x+2y+xy(x+y)[]}=3mn[2m+{m+2m2n+5}n6]=x+y{4x+2y+[xyxy]}=3mn[2mm+2m2n+5n6]=x+y{4x+2yxyxy}=3mn2m+m2m+2n5+n+6=x+y4x2y+x+y+x+y=6m+2n+1=3x+y37.{[()]17.2a+5b+(3ac)+2a+b(c+4)(a+b)}[{()[()(23.x+x+yx+yzx+yy)]}]=[x+{xy[x+yz+xy]y}]=2a+{[5b+3ac+2(a+bc4)]+ab}=2a+{[5b+3ac+2+ab+c+4]+ab}=[x+{xy+xy+zx+yy}]=2a+{5b3a+c2a+bc4+ab}=[xx2y+z]=2a5b3a+c2a+bc4+ab=x+x+2yz=2yz=a5b6[{()()[()]}]24.a+a+abab+ca+b[()]{18.3x+x(2y3)+(2x+y)+(x3)+2(x+y)}=[a+{a+aba+bc[a+b]}]=[3x+(x2y+3)]+{2xyx3+2xy}=[a+{acab}][]=3xx2y+32xyx3+2xy=3x+x+2y34x2y1=[aacab]=3a+b+c=4EJERCICIO33[][]{[19.(a)+(a)+b+c+(c)][]}[]{[]}=[a]a+bcc1.ab+cd=a+a+{bc+c}(=a+b+cd)=bc+c2.x3xyy+622=b=x2+(3xyy2+6){[]}{[20.(a+b)+(ba)(a+b)]}3.x3+4x23x+1={[ab]}{+[b+a]}ab=x3+(4x23x+1)={a+b}{b+a}ab4.a35a2b+3ab2b3=abbaab=a3+(5a2b+3ab2b3)=3a3b5.xx+2x2x+1432{[]}{[]}[{21.(a+bc)+(ca+b)+a+(b)}]=x4x3+(2x22x+1)={[ab+c]}{+[c+ab]}+[{ab}]6.2a+bc+d[={a+bc}{c+ab}+a+b](=2ab+cd)=ab+c+ca+b+a+b=a+b+2c7.x+x+3x432=x3(x23x+4)[{22.3m+mnm+4(())}+{(m+n)+(2n+3)}]8.x35x2y+3xy2y3=[3m+{m(nm4)}+{mn2n+3}]=x3(5x2y3xy2+y3)=[3m+{mn+m+4}mn2n+3]9.ax2xyy222=[3mmn+m+4mn2n+3]=a2(x2+2xy+y2)=3m+m+nm4+m+n+2n3=2m+4n710.a+b2bcc222=a2(b2+2bc+c2)38.EJERCICIO341.x+2y+(xy)6.2a+(3a+b)[=x2y(xy)][=2a(3a+b)]2.4m2n+3(m+n)+(2mn)[=4m2n3+(m+n)(2mn)]2(7.2x+3xyy+xy+x+y2)(22)[=2x23xy+(y2+xy)(x2+y2)]3.x3xy+xxy+y2[()]22=x2{3xy[(xxy)+y]}228.x33x2+4x2[]4.x33x2+4x+23x2x+3()=x3+3x2+4x2{}[[]=x33x24x+2+3x+(2x+3)]{[()]}5.2a+3b2a+a+ba9.[m(3m+2m+3)]+(2m+3)42={[m(3m+2m+3)](2m+3)}=2a[3b+{2a+[a+(ba)]}]42EJERCICIO3517.ambn{ab=am+1bn+11.2{3=618.5ambn{6a2b3x=30am+2bn+3x2.4{8=3219.xmync{xmyncx=xm+myn+nc1+x=x2my2nc1+x3.15{16=24020.mxna{6m2n=6mx+2na+14.ab{ab=a1+1b1+1=a2b25.2x2{3x=6x2+1=6x3EJERCICIO366.4a2b{ab2=4a2+1b1+2=4a3b37.5x3y{xy2=5x3+1y1+2=5x4y31.am{am+1=am+m+1=a2m+18.a2b3{3a2x=3a2+2b3x=3a4b3x2.xa{xa+2=xa+a+2=x2a+29.4m2{5mn2p=20m2+1n2p=20m3n2p3.4anbx{abx+1=4an+1bx+x+1=4an+1b2x+110.5ay{6x=30axy22224.an+1bn+2{an+2bn=an+1+n+2bn+2+n=a2n+3b2n+211.x2y3{4y3z4=4x2y3+3z4=4x2y6z45.3an+4bn+1{4an+2bn+3=12a2n+6b2n+412.abc{cd=abc1+1d=abc2d6.3x2y3{4xm+1ym+2=12x2+m+1y3+m+2=12xm+3ym+513.15x4y3{16a2x3=240a2x4+3y3=240a2x7y37.4xa+2ba+4{5xa+5ba+1=20x2a+7b2a+514.3a2b3{4x2y=12a2b3x2y8.ambnc{amb2n=am+mbn+2nc=a2mb3nc15.3a2bx{7b3x5=21a2b1+3x1+5=21a2b4x69.xm+1ya+2{4xm3ya5c2=4x2m2y2a3c216.8m2n3{9a2mx4=72a2m2+1n3x4=72a2m3n3x410.5manb1c{7m2a3nb4=35m3a3n2b5c39.EJERCICIO373m2313m+131243144528.a{ab3={am+1b3=ab1.a{ab={a5b=ab=a5b45251025251055mn3327239.ab{ab2c2.mn{am61071411137252125325={am+1bn+2c=am+1bn+2c={amn=amn=amn22471498142xm+13x1m2233246264210.ab{ab3.xy{axy=axy=a2x6y49535155212x12m+122x12m+1={ab=ab1344324355135535154.mn{amn=amn=amn8540103mn4123m2n33m2n723144111.ab{a



2mbn=ab=ab5.abc{a=abc=a4bc854010875642x+1x3244x3233453112.abc{ab6.xy{a2by5=a2bx3y9=a2bx3y9117566248=2{a2x2bx1c2=a2x2bx1c2133m+11m+1777.a{am=a=a35155EJERCICIO38331xa8.m{5a2m{am5101.a{3a{a2=3a1+1+2=3a4152+x3+1+a3x+2a+4=am=am2.3x2{x3y{a2x=3a2x2+3+1y=3a2x6y50103.m2n{3m2{5mn3=15m2+2+1n1+3=15m5n49.2a{a2{3a3{4a=24a1+2+3+1=24a74.4a2{5a3x2{ay2=20a2+3+1x2y2=20a6x2y210.3b2{4a3b{ab{5a2x=60a3+1+2b2+1+1x=60a6b4x5.am{2ab{3a2bx=6am+1+2b1+x=6am+3bx+11322362+43+1111.ambx{a2{2ab{3a2x6.x{ax{a4m=axm=a6x4m235305=6am+2+1+2bx+1x=6am+5bx+1x2m324123103327.a{ab{3a4bx+112.xy{xy2{x{xy34253418m+2+44+x+1362+1+3+21+2+1384=ab=am+6bx+5=xy=xy12284EJERCICIO394.a4a+6a322.8x2y3y23.x4x+321.3x3x22x2ax32x3ab6x+2x4316ax5y6ax3y22x3+8x26x3a4b12a3b+18a2b40.5.a2ab+b2213.x33x2+5x6ab4x2a3b+2a2b2ab34x5+12x420x3+24x26.x6x8x5314.a6ax+9ax84322223ax33bx3a2x718a2x524a2x33a4bx318a3bx4+27a2bx524bx37.m43m2n2+7n4n+315.a3an+24an+1an4m3xanx24m7x+12m5n2x28m3n4xa2n+3x2+3a2n+2x2+4a2n+1x2+a2nx28.x4xy+6xy32216.x46x3+8x27x+5ax3y3a2x3ax6y4ax5y2+6ax4y33a2x7+18a2x624a2x5+21a2x415a2x39.a5ab8ab32217.3x+5xy7xy4y32234a4m2225axy4a7m2+20a6bm2+32a5b2m215a2x4y2+25a2x3y335a2x2y420a2xy5m110.aam+am218.xa+53xa+4+xa+35xa+12a2x22am+1+2am1+12am2+12xa+7+6xa+62xa+5+10xa+3=2am+1+2am2am1m+119.a83a6b2+a4b43a2b6+b811.x+3xmxm12m5a3y23x5a11y2+15a9b2y25a7b4y2+15a5b6y25a3b8y23x3m+1+9x3m3x3m1m1n+2m2n+4m1n+1m2n+220.ab+3ababmn+am3bn+612.ab+ababmn4amb33a2b4a2mbn+3+12a2m1bn+54a2m2bn+7+4a2m3bn+93am+2bn+1+3am+1bn+23ambn+3EJERCICIO4012312212ab23ab+ca2+abb21.232.3a4b3.5654.53922523a2xa23ac5ab3362+23621+242151+125102+1ax+a2+1bxa2b2xaab4631+1ac+abc25391015a3+1b+ab151815ac91262134252=a4x+a3bxa2b2x=aab44132=a2c2+abc2ac353515=ab+ab1839241.1221121212125.xxyy2ab+xy3542345533a2my8252+2522522522323638.am+abmamx+amyxyxy3+1y2+316243240610854522522122=am+abmamx+amy1331624328=x2y3xy4y52582312519.m+mnmn2n36.3a5b+6c3269323323axmn10492+131523182363+2332+21+3151+22+3323+3ax+abxacxmn+mnmnmn10101012824369333239231351=ax+abxacx=m5n3+m4n4m3n5m2n610252881224221426142324167.xxy+yxxy+xyy93535103345xya3x4y37764+3432+32+4334+41036+43534+42+31532+44+35346+3xyxy+xy10.axy+axyaxy+axy63721352135702743561382531349=xyxy+xy=a3x10y3+a3x8y5a3x6y7+axy2177721714EJERCICIO411.a+33.x+55.x+37.3x2ya1x4x+52x+ya2+3ax+5x2x23x6x24xya34x205x+15+3xy2y2a2+2a3x+x202x28x+156x2xy2y22.a34.m66.a28.5x4ya+1m5a33x+2ya23am26ma2+2a15x2+12xya35m+30+3a+6+10xy8y2a2a32m11m+302a2+5a+615x2+22xy8y242.9.5a7b11.a+b13.9m+8na+3b8a4b6m+4n5a27ab8a2+8ab54m2+48mn+15ab21b2+4ab4b236mn+32n25a2+8ab21b28a2+12ab4b254m2+12mn+32n210.7x312.6m5n14.7y32x+4mn2y1114x26x6m25mn14y26y+28x126mn+5n2+77y+3314x+22x1226m11+5n2mn214y+71y+332EJERCICIO421.x+xy+y5.a+aa9.mm+m2223232xya1am+ax3+x2y+xy2a4+a3a2am4am3+am22amxyxyy223aa32+a+am3am2+am2ax3y3a42a2+aam4am2a6.m+mn+n10.3a5ab+2b42242.a2ab+b2222abmn224a5ba32a2b+ab2m6+m4n2+m2n412a320a2b+8ab2a2b+2ab2b3m4n2m2n4n615a2b+25ab210b3a33a2b+3ab2b3m6n612a335a2b+33ab210b37.x2x+3x1323.a+2ab+b11.5m3mn+n224224a+b2x+33mna3+2a2b+ab22x44x3+6x22x15m59m3n2+3mn4+ab+2ab+b223+3x6x+9x3325mn4+3mn23n5a3+3a2b+3ab2+b32x4x3+7x315m55m4n9m3n2+3m2n3+3mn4n512.a+a+124.x3x+19.3y6y+5323x+3y2+2a2a1x43x3+x3y56y3+5y2a4+a3+a2+3x9x32+3+6y312y+10a3a2ax49x2+x+33y5+5y212y+10a2a1a4a22a143.13.x3+2x2x19.x22xy+y2x22x+5x2+xy+3y2x+2xx543x4+2x3yx2y22x4x+2x432+x3y2x2y2+xy3+5x+10x5x32+3x2y26xy3+3y4x5+12x25xx4+3x3y5xy3+3y420.n2n+1214.m3mn+2mn322m2mn8n22n21m53m4n+2m3n2n42n3+n22m4n+6m3n24m2n3n2+2n18m3n2+24m2n316mn4n42n3+2n1m5mn54+20mn16mn23415.x2+x+121.a3ab+4ab322x2x1a2b2ab210b3a5b3a4b2+4a3b3x4+x3+x22a4b2+6a3b38a2b4x3x2x10a3b3+30a2b440ab5x2x1a5b5a4b2+22a2b440ab5x4x22x116.x3x+24222.8x312x2y+6xy29y3x22x+32x+3yx63x4+2x216x424x3y+12x2y218xy32x5+6x34x+24x3y36x2y2+18xy327y4+3x49x2+616x424x2y227y4x62x5+6x37x24x+623.2y3y+y43217.m3+m24m12y+5m3+14y46y3+2y28ym6+m54m4m3+10y315y2+5y20+m3+m24m14y+4y313y23y204m6+m54m4+m24m124.a+2ax+3x32318.a5a+23aa+522a23axx2a55a3+2a22a5+4a3x2+6a2x3a4+5a2a2+3ax46a2x39ax4+5a325a+10+ax322ax43x5a5a4+7a227a+102a+3ax+5ax543211ax43x544.30.y2y+1225.x43x3y+2x2y2+xy3x2xyy2y42y2+2x6+3x5y2x4y2x2y3y62y5+y4x5y+3x4y22x3y3x2y42y4+4y32y2x4y2+3x3y32x2y4xy5+2y24y+2x6+2x5y3x2y4xy5y62y5y4+4y34y+231.m3m+44226.a35a2+2a3a2a733m32m+1a65a5+2a43a33m79m5+12m32a4+10a34a2+6a2m5+6m38m7a+35a14a+2132+m43m2+4a5a65+31a8a+2123m11m+m+18m3m8m+47543227.m+mm+332.a+aa+143232m2m+32a+a22a13m6+m5m4+3m2a6+a5a4+a32m52m4+2m36m+a+a54a3+a2+3m4+3m33m2+92a42a3+2a22am6m5+5m36m+9a3a2+a1a6+2a52a43a3+2a2a128.a4+a3b3a2b2ab3+b433.8x12xy6xy+y3223a22ab+b23x22xy+4y2a6+a5b3a4b2a3b3+a2b424x536x4y18x3y2+3x2y32ab2ab+6ab+2ab2ab5423324516x4y+24x3y2+12x2y32xy4+ab+ab3abab+b42332456+32x3y248x2y324xy4+4y5a6a5b4a4b2+6a3b33ab5+b624x552x4y+38x3y233x2y326xy4+4y529.x4x3y+x2y2xy3+y434.5a4a+2a3a1432x2+xy2y2a42a2+2xxy+xy6542xy33+xy245a84a7+2a63a5a4+x5yx4y2+x3y3x2y4+xy510a6+8a54a4+6a3+2a22xy+2xy42332xy+2xy2y2456+10a48a3+4a26a2x62x4y2+2x3y32x2y4+3xy52y65a84a78a6+5a5+5a42a3+6a26a245.35.xx+xx+143240.3a56a3+2a23a+2x2x+3x+632a43a2+4a5x7x6+x5x4+x33a96a7+2a63a5+2a49a7+18a56a4+9a36a22x6+2x52x4+2x32x2+12a624a4+8a312a2+8a+3x53x4+3x33x2+3x15a5+30a310a2+15a10+6x46x3+6x26x+63a915a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3y+5z43224m3+3m2n5mn2+n3x+y+2zm7+2m6n3m5n2+4m3n42x2+3xy5xz+3mn6mn+9mn6524312m2n5+2xy3y2+5yz5m5n2+10m4n315m3n4+20mn6+m4n32m3n4+3m2n54n7+4xz6yz+10z2m7+5m6n14m5n2+20m4n313m3n49m2n5+20mn64n72x2+5xyxz3y2yz+10z239.x63x4y2x2y4+y644.x2xyxz+y2yz+z2x2xy+3xy5324x+y+zx113x9y2x7y4+x5y6x3x2yx2z+xy2xyz+xz22x9y2+6x7y4+2x5y62x3y8+x2yxy2xyz+y3y2z+yz2+3x7y49x5y63x3y8+3xy10+xz2xyzxz2+y2zyz2+z3x115x9y2+8x7y46x5y65x3y8+3xy10x33xyz+y3+z346.x1x2EJERCICIO437.a+3a2axx2axax1+ax+2x+11.aa+axa2x+3a2x12a2x2a+1a2x13a2x2+2a2x3ax+3ax+2+ax+1+a2x2+3a2x32a2x4+ax+2ax+1+axa2x+2a2x14a2x2+5a2x32a2x4x+3a+axa+48.mma+32ma+2+ma+12.xn+3+2xn+2+xn+1a3ma1+ma2+mx+x2m2a+3+m2a+2+2m2a+1m2axn+5+2xn+4+xn+3+m2a+2m2a+12m2a+m2a1xn+4+2xn+3+xn+2+m2a+1m2a2m2a1+m2a2xn+5+xn+4+3xn+3+xn+22a+32a+2m+2m+2m2a+14m2am2a1+m2a2a+2a+1a13.m+mm+mam22m+39.xa1+2xa2xa3+xa4a3ma+4+ma+3ma+2+ma+1xa1xa2x2ma+32ma+2+2ma+12max2a2+2x2a3x2a4+x2a5a+2a+1a1+3m+3m3m+3max2a32x2a4+x2a5x2a6ma+4ma+3+6ma+15ma+3ma1x2a42x2a5+x2a6x2a7x2a2+x2a34x2a4x2a7n+2n+14.a+3a2ann+1a+ann12n23n3410.abab+2ababn2n+32n+22n+1a+3a2aanb2an2b4+a2n+2+3a2n+12a2na2nb3a2n1b4+2a2n2b5a2n3b6a2n+3+4a2n+2+a2n+12a2na2n2b5+a2n3b62a2n4b7+a2n5b8a2nb3a2n1b4+a2n2b52a2n4b7+a2n5b85.xa+2+2xa+1xaxa+32xa+111.ax+bxx2a+5+2x2a+4x2a+3am+bm2a+32a+22a+12x4x+2xam+x+ambx2a+5x+2x2a+43x2a+34x2a+2+2x2a+1+axbm+bm+xm+xa+ab+axbm+bm+xmxx1x26.a2ax+3aa2+2a1x1n112.abx+2x+1a2a+3axabx+1+2a4ax+6ax1axabn1x1x2a+2ax3aax1b+bnx+2x1x2a2a+8ax3aaabxn1ax1b+bn47.13.5am++am++3am222126a3m18a3m2+a3m330a5m+1+6a5m+18a5m1+40a5m8a5m124a5m25a5m1+a5m2+3a5m330a5m+1+46a5m+5a5m123a5m2+3a5m3a+2x1a+1xax+114.xy4xy+3xy2x2a1yx24x2a2yx110x2a3yx2x3a+1y2x3+8x3ay2x26x3a1y2x14x3ay2x2+16x3a1y2x112x3a2y2x10x3a1y2x1+40x3a2y2x30x3a3y2x+12x3a+1y2x3+4x3ay2x2+28x3a2y2x30x3a3y2x+1EJERCICIO4412113.xxy+y2234111.ab2323xy3211a+b2322232xxy+xy26912121aab3232369xy+xyy346811+abb2238+2722+623346xxy+xyy63612812491aabb2133528336366=xxy+xyy2336128151=a2+abb21335222336366=xxy+xyy3363822.xy12254.aab+b24315x+y1336ab42122xxy13122315aab+ab2164125102+xyy323263630ab+abb82612425102xxyy132+322+18233030aab+abb3168121211=x2+xyy213522023303=aab+abb316812171=x2+xyy2135253103=aab+ab2b168348.221132125.m+mnn26.x+x532845321mmn+2n22xx+23236433322652443m+mnmnx+xx106484521133122m3nm2n2+mn3xx+x53224121542246224+m2n2+mn3n+x+x532845641512345+2048223+42652496+15321828+304m+mnmn+mn3n4x+xxx+x10306062841202460564331722735141113162384=m+mnmn+mn3n4=x+xx+x+x10306064212024605341317227351437322194=m+mnmn+mn3n4=x+xx+x+x5106064240330523112113xx2y+xy7.2x+3ax+2a8.2275212252xxy+y322436xax+a2232514132xxy+xy343392228208x+ax+ax44232223464xy+xyxy2115611223+ax3axa3x10325235232+xyxy+xy4423012222264ax+a3x+a25x21+804xy+105+112+2003210+5235xyxy+xy4696284208403012343+3327442227436=25x1014xy+417321523xyxy+5xy4x+ax+axax+a428420840301246121861510141393212353619222336=xxy+xyxy+xy4=x4+ax3+axax+a4144202802124612186341922233=x+ax+3axax+a4412181312119.x+xx+43423211x+x210535343332x+xx+x86841413121+x+xx+x40304020131211xx+x201520103560+34454+63903821+11x+xx+x+x812012012020103634473792213521447379211=x5+xx+x+x=x+xx+x+x81201201202010840120120101049.312110.4m2mn+5mn4n32232225mmn+n23326524432223mmn+mnmn1261512642324232mn+mnmn+mn4126151215325231055+mnmn+mn4n84108654+6432+40+2253210+16+752320+1205mmn+mnmn+mn4n5121212060120815104297321012314055155499321012375=mmn+mnmn+mnn=mmn+4mnmn+mn4n521212060120826406068EJERCICIO454.m5mn+6mn+nporm4mnn32233231.xx+xporx132211+115+6+11+011+04111+115+6+11+114+202441+56111+0+11=x5x4+x2x15+2+2019101=m65m5n+2m4n2+20m3n319m2n410mn5n62.x+3x5x+8porx2x7432325.x8x+3porx+6x542421+35+0+81+08+0+312+071+0+6+051+35+0+81+08+0+326+10+016+6+048+0+18721+35+0565+0+40+0151+111+313+19+0561+02+050+0+58+015=x7+x611x5+3x413x3+19x256=x82x650x4+58x2156.a63a46a2+10pora84a6+3a42a23.a+3ab2ab+5abb432234pora2ab+b221+03+06+0+101+32+511+04+0+3+0212+11+03+06+0+101+32+514+0+12+0+24+04026+410+2+3+09+018+0+30+1+32+512+0+6+0+12+0201+17+1213+711+07+0+9+0+23+052+0+42+020=a+ab7ab+12ab13ab+7abb6542332456=a147a12+9a10+23a852a6+42a420a250.8.m7m+9m15porm5m+9m4m+312841612847.x94x6+3x32por3x68x3+1017+9151+0+04+0+0+3+0+0215+94+33+0+08+0+0+1017+9153+0+012+0+0+9+0+065+3545+758+0+0+32+0+024+0+0+16+963+81135+10+0+040+0+0+30+0+0204+2836+603+0+020+0+0+51+0+070+0+0+46+0+020+321+2745=3x1520x12+51x970x6+46x320112+53127+187192+8745=m2812m24+53m20127m16+187m12192m8+87m44510.6a4a+6a2pora2a+a752429.x53x4y6x3y24x2y3y5por2x2+4y26+0+04+621364+011+02+172+0+46+0+04+6226128+0212+0+0+812+4+4122416+04+6+0+04+62268202418+0442+0+0+2842+14=2x76x6y8x5y220x4y324x3y418x2y54y76+012+236+616+3844+14=6a912a7+2a636a5+6a416a3+38a244a+1412.3x44x3yy4porx35xy2+3y311.n3n+5n8n+4porn3n+46434234+0+011+03+5+08+41+05+31+03+0+434+0+011+03+5+08+415+20+0+0+53+0+915+0+2412+912+0+03+4+012+20+032+163415+2913+0+531+06+5+13238+441232+16=3x74x6y15x5y2+29x4y313x3y4+5xy63y7=n106n8+5n7+13n623n58n4+44n312n232n+1613.x105x6y4+3x2y86y10porx64x4y25x2y4+y61+0+0+05+0+0+0+3+061+04+05+0+11+0+0+05+0+0+0+3+064+0+0+0+20+0+0+012+0+245+0+0+0+25+0+0+015+0+30+1+0+0+05+0+0+0+3+061+04+010+0+21+0+28+023+0+9+0+33+06x164x14y210x12y4+21x10y6+28x8y823x6y10+9x4y12+33x2y14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11+05+06131564+2+165+36+030+0366186304+0+20+0+245+15+5+25+2+010+012+39315+1+05+06623+1234+22156428+2146+19126=6a5x+323a5x+2+12a5x+134a5x+22a5x115a5x2=6x2a+34x2a+228x2a+1+21x2a46x2a1+19x2a212x2a36x2a4EJERCICIO46()(4.x+1x1x+1222)()()(6.aba2ab+ba+b22)()(1.4a+5a3)()x+12a22ab+b24a+20x2+1a+ba3x4+x2a32a2b+ab24a2+20a+x2+1+a2b2ab2+b312a60x4+2x2+1a3a2bab2+b34a2+8a60abx21a4a3ba2b2+ab3x6+2x4+x2(2.3ax+1x12)()x42x21a3b+a2b2+ab3b43a2x+3a2a42a3b+2ab3b4x6+x4x21x13a2x2+3a2x3a2x3a23a2x23a2()(5.mm4m63m+2)()()(7.3xx22x+1x1x+1)()m4m23x6x+3x32m6x1()(3.2a3a1a+4)()m34m23x46x3+3x22a66m2+24m3x3+6x23xa1m10m+24m323x49x3+9x23x2a26a3m+22a+6x+13m430m3+72m22a28a+63x59x4+9x33x2+2m320m2+48ma+4+3x49x3+9x23x3m428m3+52m2+48m2a38a2+6a3x56x4+6x23x+8a32a+2422a326a+2452.11.(x3)(x+4)(x5)(x+1)()(8.xx+1x+x1x222)()x3x5x2x+1x+4x+1x2+x1x23xx25x+4x12+x5x4x3+x2x2+x12x24x5+x3x2+xx24x5x2+x1x4+x312x2x4x2+2x14x34x2+48xx25x25x+60x5x+2xx32x43x321x2+43x+602x4+2x4x+2212.(x3)(x+2x+1)(x1)(x+3)222x2xx+4x25x+2543x+2x+12x23x2+3x1x+2x+x432x33x9.(a3)(a+2)(a1)mm1m1+3x2+6x+3x2+3a3mx4+2x3+4x2+6x+3x3x23x+3am1+2x3x23x+32m1m1+a3ax7+2x6+4x5+6x4+3x32am6x62x54x46x33x22m1m12a+am3a63x56x412x318x29xam11+3x4+6x3+12x2+18x+92m13m22m2m12a+a3a6ax+xx765x49x39x2+9x+92m1m1a+3a2a+6m13.9a(3a2)(2a+1)(a1)(2a1)22m13m22m2m1a+a3a3a2am+627a318a22a1 a3m2+a2m13a2m22am3am1+62a+1a154a436a32a2a+27a18a322a+1(10.aa1a2a3)()()54a9a18a4322a3a+12a2a2a23a+1a2108a618a536a4a3a2162a5+27a4+54a32a+2a2+54a49a318a2a3a+2a32108a180a+45a445a318a265a3a43a3+2a2x+114.aa+bx(x+2)(ax+1bx+2)bx2x+1x+2a+abx3a3+9a26ax+1xabb2x+2a46a3+11a26aa3x+2bx+a2x+1b2x+2a2x+1b2x+2axb3x+4a3x+2bxaxb3x+453.EJERCICIO47()2(11.3x+y4xy+3x23y2)21.4(x+3)+5(x+2)=3(x+y)(x+y)4(xy)(xy)+3x23y2=4x+12+5x+10=3(x2+xy+xy+y2)4(x2xyxy+y2)+3x23y2=9x+22=3(x2+2xy+y2)4(x22xy+y2)+3x23y2()(2.6x+43x+1+5x+2222)()=3x2+6xy+3y24x2+8xy4y2+3x23y2=6x+243x3+5x+10222=2x2+14xy4y2=8x+31212.(m+n)(2m+n)+(m4n)2223.a(ax)+3a(x+2a)a(x3a)=a2ax+3ax+6a2ax+3a2=(m+n)(m+n)(2m+n)(2m+n)+(m4n)(m4n)=10a+ax2=m2+2mn+n2(4m2+4mn+n2)+m28mn+16n24.x(y+1)+y(x+1)3xy222222=2m26mn+17n24m24mnn2=2m210mn+16n2=x2y2+x2+x2y2+y23x2y2=x2y2+x2+y2()()()(13.xa+x+3xa+1x+1a+2xax)()25.4m5mn+3m(m+n)3m(mn)+3ax+3x(ax+2x+a+2x)(ax)(ax)3222222=ax+x22=4m35mn2+3m4+3m2n23m3+3mn2=4ax+x+3xax2x22a2x(aaxax+x)22=3m4+m3+3m2n22mn2=3axx2+xaa2+ax+axx2233222(6.y+xyyx+1+yx+1yx1222)()()=2x2+x+5axaa2=y2+x2y3x2y3y3+x2y2+y2x2y2+y2=y3+3y214.(a+bc)+(ab+c)(a+b+c)222()()()7.5x+2x+1x+46xa+bcab+c=5x+10(x+4x+x+4)6x2a+bcab+ca2+abaca2ab+ac=x+10x24xx4+ab+b2bcab+b2bc=x26x+6acbc+c2+acbc+c28.(a+5)(a5)3(a+2)(a2)+5(a+4)a+2ab2ac+b2bc+c222a2ab+2ac+b22bc+c22=a25a+5a253(a22a+2a4)+5a+20a+b+c=a2+5a53(a24)a+b+c=a2+5a53a2+12a2+ab+ac=2a2+5a+7+ab+b2+bc9.(a+b)(4a3b)(5a2b)(3a+b)(a+b)(3a6b)+ac+bc+c2=4a2+ab3b2(15a2ab2b2)(3a23ab6b2)a+2ab+2ac+b+2bc+c222=4a2+ab3b215a2+ab+2b23a2+3ab+6b2a2+2ab2ac+b22bc+c2=14a2+5ab+5b2a22ab+2ac+b22bc+c2()()10.a+cac22a22ab2acb22bcc2=(a+c)(a+c)(ac)(ac)a22ab2ac+b26bc+c2=a+ac+ac+c(aacac+c)2222 a2+b2+c22ab2ac6bc=a2+2ac+c2a2+ac+acc2=4ac54.()(215.x+x3x2+x+xx3222)(2)2()(216.x+y+zx+yxy+3x+xy+y22)()()x+x32x+x22x+y+zx+yx+y+zxyx+x32x2+x2x2+xy+xzx2+xyx4+x33x2x4+x32x2+xy+y2+yzxyy2+x3+x23x+x3+x22x3x23x+92x22x+4+xz+yz+z2x2y2x4+2x35x26x+9x4+2x33x24x+4x+2xy+2xz+y+2yz+z222x2x3x2+2xy+2xz+y2+2yz+z2x2x3x2+y23x+3xy2+3y2x4x33x2x4+2x35x26x+9x3+x2+3xx42x3+3x2+4x43x2+5xy+2xz+5y2+2yz+z23x2+3x+9x42x35x2+6x+9 3x2+5y2+z2+5xy+2xz+2yzx42x35x2+6x+9x42x37x2+4x+14[18.3(x+2)4(x+1)3(x+4)2(x+2)][][][17.x+(2x3)3x(x+1)+4xx2][][=3x+64x43x+122x4][][]=x+2x33xx1+4xx2=[x+2][x+8]=[3x3][2x1]+4xx2=x28x+2x+16=6x23x6x+3+4xx2=x26x+16=5x5x+3220.[(x+y)3(xy)][(x+y)(xy)+x(yx)]22[()()][()()])(19.m+nmnm+nm+n2m+n3mn)([][=x2+2xy+y23(x22xy+y2)x2y2+xyx2]=[mn(m+2mn+n)][2m+2n3m+3n][][xyy]2222=x+2xy+y3x+6xy3y22222=[mnm2mnn][m+5n][][]2222=2x2+8xy2y2xyy2=[2mn2n][m+5n]2=2x3y+2x2y2+8x2y28xy32xy3+2y4=2m2n10mn2+2mn210n3=2x3y+10x2y210xy3+2y4=2mn8mn10n223EJERCICIO48[3.3x2y+(x2y)2(x+y)3(2x+1)][=3x2y+x2y2x2y6x3][1.x3a+2(x+1)][=4x6y3][=x3a2x+2]=4x+6y+3=x3a+2x2=3x3a2{4.4x23x+5x+x2x[)]}(=4x2{3x+5[x+2xx]}[]22.(a+b)32a+b(a+2)[=ab32aab+2b]=4x2{3x+5+x2x+x}2=ab6a+3ab6b=4x2{4x+5+x}2=7a7b+3ab 7a+3ab7b=4x2+4x5x2=3x2+4x555.{[5.2a3x+2a+3x2a+b2+a())]}([{(10.m3(m+n)+2m+n23[mn+1]+m)}]=m3m3n+[{(2m+n23m+3n3)+m}]=2a{3x+2[a+3x2(a+b2a)]}=2m3n+[{(5m+4n5)+m}]=2a{3x+2[a+3x+2a2b+4+2a]}=2m3n+[{5m4n+5+m}]=2a{3x+2[3a+3x2b+4]}=2m3n+[{6m4n+5}]=2a{3x+6a+6x4b+8}[=2m3n+6m+4n5]=2a+3x6a6x+4b8=2m3n6m+4n5=4a3x+4b8 4a+4b3x8=8m+n5[6.a(x+y)3(xy)+2(x2y)2(xy)][=axy3x+3y+2x+2y+2x+2y]=a4x+2y+2x+4y[]{[11.3(x2y)+242x3(x+y)]}{[(x+y)]}=a4x+2y+2x+8y=3x+6y+2{4[2x3x3y]}{[xy]}=a2x+10y=3x+6y+2{4[5x3y]}{x+y}=3x+6y+2{20x+12y}xy{[7.m(m+n)32m+2m+n+2(1+n)(m+n1)]}=4x+5y+40x+24y{[=mmn32m+2m+n2+2nmn+1]}=36x+29y{[=n32m+3m+2n1]}=n3{2m3m+2n1}=n3{5m+2n1}=n+15m6n+3{[12.5(a+b)32a+3b(a+b)+(ab)+2(a+b)a]}=7n+15m+3 15m7n+3{[]}=5ab32a+3babab2a+2ba{[]}=5ab36a+3ba{[8.2(ab)3(a+2b)4a2b+2a+b1+2(ab)]}=5{2ab+18a9b}=2a+2b3a6b4{a2b+2[a+b1+2a2b]}=5{16a10b}=5a4b4{a2b+2[ab1]}=80a50b=5a4b4{a2b+2a2b2}=5a4b4{3a4b2}=5a4b12a+16b+8{[13.3+(a+b)]}4{[(ab)]}=3{[a+b]}4{[a+b]}=17a+12b+8=3{ab}4{ab}[{}]9.5(x+y)2xy+2x+y3(xy1)+2x=3a+3b+4a+4b=5x5y[2xy+2{x+y3x+y+1}]+2x=a+7b=3x5y[2xy+2{2x+2y2}][=3x5y2xy4x+4y4]{{[]}[14.a+b
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2(ab)+32a+b3(a+b1)3a+2(1+a)]}=3x5y[2x+3y4]={a+b2a+2b+3{[2a+b3a3b+3]}3[a2+2a]}=3x5y+2x3y+4=x8y+4={a+3b+3{a+2b3}3a+6}={4a+3b+6+3a+6b9}={a+9b3}=a9b+356.EJERCICIO4918944112.abc8c==a8b98944abc881.248=316643162.637=913.16mn5n=643mn=m6n553.5a2a=5a21=5a1087668827714.108abc20bc==76868abca4.14a3b42ab2=7a31b42=7a2b22055.a3b4ca3b4=a33b44c=c22166215.2mn3mn=mn=m2666.abab=a2111332b=a16.axa2=ax27.54xyz6xyz=9x21y22z33=9x2232317.3axbmab2=3ax1bm28.5m2nm2n=5m22n11=55m3n41159.8a2x38a2x3=a22x33=118.5abc6abc=mn34abc=am3bn466xy21xy10.xy2y==21xmmn19.ab4ab=xmmn22ab454451511.5xy6xy=xy=y4454axx2333320.3mnx5mnx=mnxax3x23=maxnx26655EJERCICIO502.2xa+4xa+2=2xa+4b+2g=2xa+4a2=2x2a1.am+3am+2=am+3m+2bg=am+3m2=a12n+3b+4g112n+34xn+4==x2n+3n4=xn1n4.xx3m2b5g3m2m+533444m23.3a5am5==a=ama555m+3m17m+34m127m1m36.7xy8x4y2=xy=xyx2n4x23n24x5n2885.4ab5ab=b=ab32a55n1n+1n1n+14n1n+1n+1n148.4xy5xy=xy=55557.5a2m1x3b6a2m2bx4=a2m12m+2bx3x+4=ab6651m2n3x10.5abc6abc=23mnxabc9.am+nbx+aamba=am+nmbx+aa=anbx6EJERCICIO51112222322x=x=x1.23245.2x4y52=9x4y5=2x4y5=1x4y53921891336.3m4n5p6m4np5=1m44n51p65=9n4p33342153abab=5a32b11=a=a32.5542047572565568215566=14a=7a27.8abc2abc=5abc4020253131252xyzz=3xy5z33=xy=4xy53.3613622xm3210x1m278.abab=3ax1bm2=ab35397mn328m1n27m1n2abab2=8am1bn2=ab=ab54.843246457.311.2ax+4bm31a4b3=2ax+44bm33=4axbm63353x21cdd=8c3d5x=12c3d5x=1c3d5x9.843242241312.ax3bm+5c2ax4bm131553mn36mn311abb3=4ambn3=ab=ambn310.42312251=15ax3x+4bm+5m+1c2=ab6c2=ab6c2234595EJERCICIO52ax+am1axam1a2aba2ab10.=2+2=ax2+am31.aaba===ab2a2aaaaam+211.2a3am+6am+42.3xy5ax3x232423x2y35a2x43x2y35a2x45223a3===y3+ax3x23x23x232am3am+26am+42=+=am3+am12am+13a33a33a333.3a5ab6ab3223m1n+2m2n+42a12.ab+ababmn233a35ab6ab23523ab==a2+b2+3ab32a2a2a22ambnam1bn+2am2bn+4=23+aba2b3a2b3x34x2+xx34x2x4.=+=x24x+1=ab+abam4bn+1m2n3m3n1xxxxm+213.x5xm+6xm+1xm15.4x10x5x864xm22x3m+2x5xm6xm+1xm14x810x65x45=m2m2+m2m2=3=2x55x3xxxxx2x2x32x32=x45x2+6x3x 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214208436441332123xy+xyxy2135235214473792111312119.x+xx+x+xx+xx+4423212384012012010104342+xyxy+xy211533133323211x5x4+xxx+xx532123582842105xyxy+xy42161214131121xxx+x5321235406012010xy+xyxy4216121413121xx+xx40304020131211xx+x20152010131211x+xx+2015201015549932101237533122110.mmn+mnmn+mn4n5mmn+mn2n326406068425415144321232225m+mnmn+mnmmn+n22315633214533291237mn+mnmn+mn4224606141324231mnmn+mnmn423156153252355mnmn+mn4n84815325235mn+mnmn4+n5848EJERCICIO581.x5x4+x2xx3x2+x11+0+1111+13.a6+a5b7a4b2+12a3b213a2b4+7ab5b6a22ab+b21+111+011+17+1213+7112+11+11 x211+211+32+51+11+138+12 a4+3a3b2a2b2+5ab3b43+632.x7+x611x5+3x413x3+19x256x32x272+9131+111+313+19+05612+0724+21+20+71+35+0+8511+7311+1013 x4+3x35x2+85+1053+60+211+215+10+8+19+12+1+510+035816+0568+160+5667.4.m5mn+2mn+20mn19mn10mnnm4mnn654233245632315+2+20191011+04110+4+115+6+15+6+2119 m35m2n+6mn2+n35+02056+124108.m2812m24+53m20127m16+187m12192m8+87m445m127m8+9m41560+24+6112+53127+187192+874517+9151+0411+79+1515+94+310+4+15+44112+187 m165m12+9m84m4+3+535+45755.x82x650x4+58x215x4+6x25967+1121921250+58151+659+6381+13516+518+34+3157+87845+58 x48x2+3+428+3660+8+4840321+27453+18153+2127+45318+156.a147a12+9a10+23a852a6+42a420a2a84a6+3a42a217+9+2352+422014+321+43+2136+109.2x76x6y8x5y220x4y324x3y418x2y54y72x2+4y23+6+2552 a3a46a2+106268202418+042+0+4312+962041364+016+3458+4261220 x53x4y6x3y24x2y3y5+624+18126+0+121040+30201282410+4030+20+12+0+248+0187.3x20x+51x70x+46x203x8x+10151296363+8+0+16320+5170+462038+102+043+81014+322+0+412+4170 x94x6+3x321232+40930+4610.6a912a7+2a636a5+6a416a3+38a244a+14a42a2+a79+24306+012+236+616+3844+141+02+176+162060+126+426+0+04+62616+204+6+616+38 6a54a2+6a2+4+08+4286212+104460+126+422+0+42+14+204+21468.11.n6n+5n+13n23n8n+44n12n32n+16n3n+5n8n+41087654326431+06+5+13238+441232+161+03+5+08+410+350+841+03+0+43+0+131512+4412 n43n2+4+3+09+15+024+1212.3x74x6y15x5y2+29x4y313x3y4+5xy63y7x35xy2+3y34+012+20+036+163415+2913+0+531+05+34+0+12200+361630+15934+0+014+0+2013 3x44x3yy4+4+020+121+0+53105+313.x164x14y210x12y4+21x10y6+28x8y823x6y10+9x4y12+33x2y146y16x64x4y25x2y4+y61410+21+2823+9+336145+11+4+511+05+0+3614.am+23am+15am+20am125am3a255+20+2823 x105x6y4+3x2y86y10135+20+0251+05+52025+510+513+0+5318+9+333+0+20 am3am1+5am33+12+153+3+0156+24+306+5+025+62430+650+2515.7a2x+535a2x+4+6a2x+378a2x+25a2x+142a2x7a2x17ax+3+6ax+1+ax735+67854277+0+6+1706115+0735+0795 ax+25ax+17ax1+35+0+30+549+0427490+42+716.6x2a+34x2a+228x2a+1+21x2a46x2a1+19x2a212x2a36x2a46xa+14xa+2xa1+xa26428+2146+1912664+2+16+4211+05+0630+2046+19 xa+25xa6xa2+3020+10+536+241263624+12+617.6a5x+323a5x+2+12a5x+134a5x+22a5x115a5x2a2x+23a2x+1a2x5a2x1623+1234+221513156+18+6+3065+35+184+22 6a3x+15a3x+3a3x1+515525393153+9+3+1569.EJERCICIO593.9x3+6x2+73x27a2+b29x33x+2+1.a22.a4+2a33x2b2a4a+2+6x2a21+a2a36x2b2+2+74.16a420a3b+8a2b2+7ab34a29.x3x2+3x+2x2x+1316a44a25ab+2b2+7b2x+2x3+x2xx+24axx+120a3b+2x+2+20a3b8a2b210.x3+y3xy8ab222y3x3+x2yx2+xy+y2+xy+7ab3x2y5.x2+7x+10x+6x2y+xy24xy2+y3x26xx+1+x+6xy2+y3x+10x62y3+46.x25x+7x411.x5+y5xy32y5x+4x2x1+x+xy44x4+x3y+x2y2+xy3+y4+x4xyx+7x4yx4x4y+x3y2x3y2+3x3y2+x2y37.m411m2+34m23x2y310x2y3+xy4m4+3m2m28+2m3+xy4+y58m+342xy4+y58m2422y5+10x26xy+y2x+y12.x+4x5x+8x22x+1328.8y26x+2x2xyx7y+x3+2x2xx+6+x+yx22x+17xy+y26x26x+8+7xy+7y26x2+12x6+8y26x+270.14.x3x+9x2+7x4x23x+25413.8a6ab+5ab9b2a3b322312b320x108a3+12a2b4a2+3ab+7b2+x5+3x42x3x32x+3+2a3bx23x+26a2b+5ab22x3+9x2+7x6a2b+9ab2+2x36x2+4x14ab29b33x2+11x414ab2+21b33x2+9x620x1012b3EJERCICIO60Paralosproblemasdel1al9lasliteralestomanlossiguentesvalores:a=1b=2c=1/21.a2ab+b2.3a4ab+3abb3.a3a+2ac3bc22322343=(1)2(1){2+22=3(1)4(1){2+3(1)22231 1 =(1)3(1)+2(1) 3{2 23243 2 2 =1+2{2+4=1+4+4=9=34{23{48=38128=3111=1+3+2{+6{=1+3+1+3=8224.a8ac+16ac20ac+40acc5432234523454 1 3 1 2 1 1 1=(1)8(1) +16(1) 20(1) +40(1) 5 2 2 2 2 2 11111551132+131=1+8{16{+20{40{+=1+44++=1+==24816322232323232()(25.ab+bcac)(2)2()(36.b+abcac)(3)3 1 2 1 233=(12)+ 2 1 [ 1 ] 1 =2+(1) 2 1 23 2 2 2 2 1 21 2 5 1 22=(3)+ 2+ 1+ =9+ 1 31 3 5 1 33[]23 2 2 =21 2+ 1+ =13 2 2 2 2 22 2512412511243123129=9+=9+=9+6=15=1+=1=1===14214448882227.ab+acbc()(28.a+b+c

abc+c)2cba22 1 1 1 1 1 1= 1+2+ 12 + 1 2 2 2 2 1{2 2 2 222=+=+1 1 21 21 1 5 22121221= 1 3+ = 22 2 2 2 2 2 21112+11312511252=4+1=3+===341==26==62=6214444442444(

)(9.32a+b4ab+c2cab)()[] 1 1 1 2 2 2[ 3 6 2 2]=32(1)+24(1) 2+ 2 (12)=32+2+4 2 +(3)=3{0+4 =63=3 2 271.Paralosproblemas10al16lasliteralestomanlossiguientesvalores:a=2b=1/3x=2y=1m=3n=1/211.(ax)+(xy)+(xy)(m+xn)42210.xxy+3xyy32222822[][][2 1 =2(2)+2(1)+(2)(1) 3+(2) ]22(2)(2)(1)+



3(2)(1)2422(1)3 2 = 1 1 8164622[][][]=2+2+2+1+41 32 =[4]+1+3 1 22 2 22 2 []=++1=2+23+1=2822 1 334+337=16+1+3 =17+===1821 2 222()(12.xy+x2+y2xym+3bx+y+n)()()[=2(1)+(2)+(1)][22][2(1)3]+3{1 2+(1)+2 =[2+1]+[4+1][5+1]+

21+2 311 1 5 38+5 []2 2 5=1+54+ 3+ =120+ =19=2243==212214xx3 11 xy14.+ x+x4m13.(3x2y)(2n4m)+4xy223y2+y3 nb 2 (2)(1)4(2)(2) 11 3[1 2] =3(2)2(1) 2{4{3 +4(2)(1) 222=+ (2)+(2)33(1)2+(1)34 11 2+11 2

3 [][=6+2112+4{4{1]=411+16[]88+(23)(2)+163=+8+(1)(2)+13228=113213=44+16+=60+=602122888+6977=+21+2=+23===252315.x(xy+m)(xy)(x+yn)+(x+y)(m2n)222223333[ ][1 ][]2 1 =(2)2(1)+32(1) (2)+(1) +2+(1) 322{ 222 2 2 1 1 9160+9169=4[1+1][2+1] 4+1 +[21](91)=4{2[1] 5 +[3](8)=8++9{8=80+=229==8421 2 2 2222116.3a+2y+3nm+2(x3y2+4)=3{2+2(1)+3{xmyn2311()()[32]23+22312+4=3236+281+4[]24+9114+13=96[]13613+25=910=19=66=1276=2116EJERCICIO611.7am8am9am10am5.32a23a+82a23a+58a+5+5!+2!1!4!2a23a+82a2+5a+13Rta{[(())]}3.x23xyx26.3x24x2+5xx2x+63xyy2x2+y2x2y2y2Rta=3x2{[4x+5x(xx6)]}224.3x25x+6=3x2{[4x+5xx+x+6]}223x2+8x6Rta3x=3x2{3x26x6}=3x2+3x2+6x+6=6x+672.()(7.x+yxyx+y)()21311311=x2xy+xyy2(x+y)(x+y)12.aab2+ba+b4901523=x2y2(x2+2xy+y2)11a3a2b1211aab+b246235=x2y2x22xyy2121=2xy2y2abab26908.a=2b=3c=1121ab+ab2121a+ab+b2cb69253(a+b)4(cb)+a1131211ab2+ba+abb2131015235=3(2+3)4(13)+21133+14ab2bab=ab2101533=3{54(2)+2=15+8+1=23+1=2413.3ab2b3a3a2b+b39.3x25y22x2+5xy+6y22ab+3abb2232a2b+2b3x+3xyy22x5xy22a2b2b3a33a2b+3b32x+3xy6y22x2+6y2a33a2b+3b32x+3xy6y22a2ab+b2x2+6y2a53a4b+3a2b33x+3xy2Rtaab+3ab4323ab422112+ab3ab3223+3b510.aab+b325a54a4b+4a3b23ab4+3b5123a+ab2b22414.x5x+4x321413122aab+ab34106x26x+32x316x2+5x+121338x+8x32x3+19x26x+a3ba2b2+ab3282042x319x2+6xx3+3x2x+12a2b2+ab3b43514131932223324x3+3x2x+12x2x+3a+abab+abb34120205x3+x23xx+4x5x3+5x24x4x+12211.2x4+2x10x24x2+4x12+6x36x+30x2x+5x+7x16x+305432x22x+6x+2x6x543x3x+5x+7x16x(2+x)(1+x)(x2)(x2+x3)=x2(3x+10)+2(3x1)3222215.+x32x2+6x5x210x+30(4+4x+x)(1+x)(x+x22435x22x+6)=3x3+10x2+6x25x2+10x304+5x2+4x+4x3x3+5x2+2x6=3x3+10x2+6x23x3+10x2+6x2=3x3+10x2+6x273.16.x=2y=121.[x(3x+2)][x+(x+3)]22=x2(x24x+4)(7x+6)(x+y)(xy)+2(x+y)(xy)22[x2][3x2x2x+3]=x44x3+4x27x6=(2+1)(21)+2(2+1)(21)22x4x3+3x23x3+3x29x2x2+2x6=x44x3+4x27x6=(1)(3)+2(1)(3)x44x3+4x27x6=x44x3+4x27x622=1{9+2{3=9+6=15[22.x(x+y)x(xy)][2(x2]+y2)3(x2y2)17.x+2x+82=x2+xyx2+xy=2x+2y23x2+3y22x+4x2+4x+6=2xy=x2+5y2x64x8x3Rta2x2+5y22x3y+10xy3x+4x+625x24x+32xy4x3y7xy3Rta18.{3a+(b+a)2(a+b)}[2(a+b)(ab)]2xy+10xy2x3y+3xy333={3ab+a2a2b}[=2a+ba+b]={2a3b}y3xyx2+3xyy23=2[2b]23.x=2a+3b=4bx+xy32x+xy+y22x2+xy+y24bx2yx4+3x3yx2y22a3bxy+xy22+x3y+3x2y2xy32a7bRtaxy2+x2y2+3xy3y4[(19.5x+3xxy))]([8x+2x+(x+y)]xy+y23x+4xy+3x2y2+2xy3y4Rta43=5x+[(3xx+y)][=8x+2xx+y]=5x+[2xy]=8x3x+y()(24.xyx+xy+yx+yxxy+y2222)()()=5x2xy=5x+y=3xy[=x3+x2y+xy2x2yxy2y3x3x2y+xy2+x2yxy2+y3]5x+y[=x3y3x3+y3]3xy=x3y3x3y315x2+3xy=2y35xyy225.a=4b=9c=2515x2xyy+2(ba)23(cb)22Rtaab9bccab1312511214{99{9+2(94)3(259)20.x+xy+xy2+y3xxy+y22542412324=2542913121211x+xyxyx+y3681569548223=+2{53{16{=+10{48{121125163543xyxy2+y364512+2258005636123=+80===561031211521010xy+xyy32612326.x3+3x24x12x+3x24=x2[2x+5x(xy)]4x+yx3x32x42?4x12[]11=2x+5xx+yxy23+4x+12x24x28+131[=2x+6x+y]2x+3yx+2x2x+2Rta922x4=2x6x+yx+yRta232x+4=4x+y74.{(27.4x3xx(4+x)+xx+(3))}[{}]28.x+7x52222x29x411x3+21xRta=4x2{3x(x4x)}+[x{x3}]Si22x=2x+7x5x43218x14x84x+4532=4x2{3xx2+4+x}+x2x+3[]6x25x19x263x+45x4+7x314x263x+45=6(2)5(2)12=4x24x+x24+x2x+3x4+7x314x263x+45=6x5x12=6(4)+101=24+101=3330.3[x2+(3x+4)(x+3)]x+5x632[=x3x+4+x32]29.(a2+b2)(a+b)(ab)4[=a3a+2(a+2)4(a+1)a+b4]x3+5x23[=x22x+1](a2+b2)(aab+abb)=a[3a+2a+44a4a+b]2244=x2+2x1(a+b)(ab)=a[b]222244x3+5x23x2x+2aab+abb422224=ab44x+1x2+2x1ab44=ab44x3+5x2+x2Rtax+1EJERCICIO6210.(3a+8b)=9a+48ab+64b3426348()1.m+3=m2+6m+9211.(4m+5n)=16m+40mn+25n5621056122.(5+x)=25+10x+x12.(7ab

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