guia de factorizacion

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  • 1. GUIA EJERCITACIN Ayudante: Vicente Andrs Caerols G. Esta gua es de exclusiva propiedad de quien la emite. No duplicar Factorice las siguientes expresiones algebraicas.1. a 2 + 2a =2. 5a 25ab =3. xy x 2 y + xy 2 =4. x 2 y 2 =5. 3 p 2 3q 2 =6. p 2 2 pq + q 2 =7. a 2 + 10a + 25 =8. 3ax 2 3a =9. x 2 3x 4 =10. 2 x 2 + 4 x + 2 =11. x 2 + 3x 4 =12. b 2 3b 28 =13. 20abc 30abd 60b 2 c + 90b 2 d =14. 9 x 2 +12 xy + 4 y 2 =15. a 2 20a 96 =16. a 2 + 17 a + 72 =17. 144 y 2 4 z 2 =18. ax bx ay + by =19. x 3 8 = 1

2. 20. y 8 x 8 =21. 8 x 3 + 27 =22. ( a + 5) 2 b 2 =23. 6 x 2 + 7 x 5 =24. 2 x 2 + 7 x + 5 =25. 6 x 2 16 x + 10 =26. 5( a + b ) 12a( a + b ) + b( a + b ) =27. x 2 a 2 + x a 2 x =28. 2am 2an + 2a m + n 1 =29. 4am 3 12amn m 2 + 3n =30. ( x 2 + 2 )( m n ) + 2( m n ) =31. 1 + 343n 3 =32. 1 y 6 =33. x 2 4 + x 3 4 x =34. x 2 + 7 x + 6 =y235. x4 =2536. x 3 + x 5 x 7 =37. a ( n +1) b( n +1) n 1 =38. 5a 2 + a =39. m 2 + 2mx + x 2 =40. a 2 + a ab b =41. x 2 36 = 2 3. 42. 9 x 2 6 xy + y 2 =43. x 2 3x 4 =44. 6 x 2 x 2 =45. 27 x 3 1 =46. a 3 3a 2 b + 5ab 2 =47. 2 xy 6 y + xz 2 z =48. 1 4b + 4b 2 =49. 4 x 4 + 3x 2 y 2 y 4 =50. a 2 a 30 =51. 15m 2 + 11m 14 =52. a 6 +1 =53. 8m 3 27 y 6 =54. 15a 2 24ab + 9b 2 =55. 8a 3 12a 2 + 6a 1 =56. 1 a 2 b 4 =57. x 4 + 4 x 2 21 =58. a 2 + ab + ax + bx =59. ax 2bx 2ay + 4by =60. 3m 3n 2nx 4 + 2mx 4 =61. 4a 3 1 a 2 + 4a =62. 3abx 2 2 y 2 2 x 2 + 3aby 2 =63. 4a 3 x 4a 2 b + 3bm 3amx =3 4. 64. y 2 9 y + 20 =65. x 2 9 x + 8 =66. 12 8n + n 2 =67. x 2 7 x 30 =68. 20 + a 2 21a =69. x 2 15 x + 54 =70. x 2 + 2 x 80 =71. m 2 41m + 400 =72. 4 x 2 12 xy + 9 y 2 =73. 1 2a 3 + a 6 =74. 16 + 40 x 2 + 25 x 4 =75. 100 x 10 60a 4 x 5 y 6 + 9a 8 y 12 =76. 3a 2 b + 6ab 5a 3 b 2 + 8a 2 bx + 4ab 2 m =77. ( a + 3)( a +1) 4( a +1) = 478. 1 a = 8 979. 4a 2 n b 4 n =80. x 6 + 4 x 3 77 =x2 y681. =4 8182. 3ax 2 3a =83. 3 x 2 3 x 6 =84. 2a 2 x 4abx + 2b 2 x =4 5. 85. 2a 3 2 =86. a 3 3a 2 28a =87. x 3 4 x + x 2 4 =88. 3ax 3 + 3ay 3 =89. 4ab 2 4abn + an 2 =90. x 4 3x 2 4 =91. a 3 a 2 a + 1 =92. 2ax 2 4ax + 2a =93. x 3 x + x 2 y y =94. 2a 3 + 6a 2 8a =95. 16 x 3 48 x 2 y + 36 xy 2 =96. 3 x 3 x 2 y 3xy 2 + y 3 =97. 5a 4 + 5a =98. 6ax 2 ax 2a =99. n 4 81 =100. 8ax 2 2a =101. ax 3 + 10ax 2 + 25ax =102. x 3 6 x 2 7 x =103. m 3 + 3m 2 16m 48 =104. x 3 6 x 2 y +12 xy 2 8 y 3 =105. ( a + b ) ( a 2 b 2 ) ( a 2 b 2 ) =106. 32a 5 x 48a 3 bx + 18ab 2 x = 5 6. 107. x 4 x 3 + x 2 x =108. 4 x 2 + 32 x 36 =109. a 4 ( a + 2) 2 =110. x 6 25 x 3 54 =111. a 6 + a =112. a 3 b + 2a 2 bx + abx 2 aby 2 =113. 3abm 2 3ab =114. 81x 4 y + 3 xy 4 =115. a 4 a 3 + a 1 =116. x 3 x 2 18 x 3 =117. 6ax 2bx + 6ab 2b 2 =118. am 3 7 am 2 + 12am =119. 4a 2 x 3 4a 2 =120. 28 x 3 y 7 xy 3 =121. 3abx 2 3abx 18ab =122. x 4 8 x 2 128 =123. 18 x 2 y + 60 xy 2 + 50 y 3 =124. ( x 2 2 xy )( a + 1) + y 2 ( a + 1) =125. x 3 + 2 x 2 y 3 xy 2 =126. a 2 x 4b 2 x + 2a 2 y 8b 2 y =127. 45a 2 x 4 20a 2 =128. a 4 ( a 12 ) 2 = 6 7. 129. bx 2 b x 2 + 1 =130. 2 x 4 + 6 x 3 56 x 2 =131. 30a 2 55a 50 =132. 9( x y ) 3 ( x y ) =133. 6a 2 x 9a 3 ax 2 =134. 64a 125a 4 =135. 70 x 4 + 26 x 3 24 x 2 =136. a 7 + 6a 5 55a 3 =137. 16a 5 b 56a 3b 3 + 49ab 5 =138. 7 x 6 + 32a 2 x 4 15a 4 x 2 =139. x 2 m +2 x 2 y 2 n =140. 2 x 4 + 5 x 3 54 x 135 =141. ax 3 +ax 2 y + axy 2 2ax 2 2axy 2ay 2 =142. ( x + y ) 4 1 =143. 3a 5 + 3a 3 + 3a =144. 1 a 8 =145. a 6 1 =146. x 4 41x 2 + 400 =147. a 4 2a 2 b 2 + b 4 =148. x 5 + x 3 2 x =149. 2 x 4 + 6 x 3 2 x 6 =150. 3 x 4 243 = 7 8. 151. 16 x 4 8 x 2 y 2 + y 4 =152. 9 x 4 + 9 x 3 y x 2 xy =153. 12ax 4 + 33ax 2 9a =154. x 8 y 8 =155. x 6 7 x 3 8 =156. 64 x 6 =157. a 5 a 3 b 2 a 2 b 3 + b 5 =158. 8 x 4 + 6 x 2 2 =159. a 4 25a 2 + 144 =160. a 2 x 3 a 2 y 3 + 2ax 3 2ay 3 =RESPUESTAS: 9. ( x 4)( x +1)1.a( a + 2 ) 10. 2( x +1) 22. 5a (1 5b ) 11. ( x + 4)( x 1)3. xy (1 x + y ) 12. ( b 7 )( b + 4 )4. ( x y )( x + y )13. 10b( a 3b )( 2c 3d )5. 3( p q )( p + q ) 14. ( 3 + 2 y ) 26. ( p q ) 2 15. ( a 24)( a + 4 )7. ( a + 5) 216. ( x + 9)( x + 8)8. 3a( x 1)( x +1)17. 4( 6 y z )( 6 y + z ) 8 9. 18. ( a b )( x y )40. ( a +1)( a b )19. ( x 2) ( x + 2 x + 4 )241. ( x 6 )( x + 6 )20. ( y 4 + x 4 )( x 2 + y 2 )42. ( 3 x y ) 221. ( 2 x + 3) ( 4 x 2 6 x + 9)43. ( x 4)( x +1)22. ( a + 5 b )( a + 5 + b )44. ( 3 x 2 )( 2 x +1)23. ( 3 x + 5)( 2 x 1)45. ( 3 x 2)( 2 x +1)24. ( 2 x + 5)( x +1)46. a ( a 2 3ab + 5b 2 )25. 2( x 1)( 3 x 5)47. ( x 2 )( 3 y + z )26. ( a + b )( 5 12a + b )48. (1 2b ) 227. ( x + 1) ( x a 2 )49. ( x 2 + y 2 )( 2 x + y )( 2 x y )28. ( m n +1)( 2a 1)50. ( a 6 )( a + 5)29. m( m 3)( 4am 1)51. ( 5m + 7 )( 3m 2 )30. ( m n ) ( x + 4 )252. ( a 2 + 1)( a 4 a 2 + 1)31. (1 + 7 n ) (1 7 n + 49n 2 )53. ( 2m 3 y 2 )( 4m 2 + 6my 2 + 9 y 4 )32. (1 y )(1 + y ) (1 + y + y 2 )(1 y + y 2 )54. 3( a b )( 5a 3b )33. ( x + 2 )( x 2)(1 + x )55. ( 2a 1) 334. ( x + 6)( x + 1)56. (1 ab 2 )(1 + ab 2 ) y y35. x + x 22 5 557. ( x 2 + 7 )( x 2 3)36. x 3 (1 + x 2 x 4 )58. ( x a + b )( a + x )37. ( n +1)( a b 1)59. ( a 2b )( x 2 y )38. a( 5a +1) 60. ( m n ) ( 3 + 2 x 4 )39. ( m + x ) 2 61. ( 4a 1) ( a 2 + 1)9 10. 82. 3a( x +1)( x 1)62. ( x + y 2 2 )( 3ab 2) 83. 3( x +1)( x 2 )63. ( ax b ) ( 4a 3m )2 84. 2 x( a b ) 264. ( y 5)( y 4 ) 85. 2( a 1) ( a 2 + a + 1)65. ( x 8)( x 1) 86. a( a 7 )( a + 4 )66. ( n 6 )( n 2) 87. ( x + 1)( x + 2)( x 2)67. ( x 10 )( x + 3) 88. 3a ( x + y ) ( x 2 xy + y 2 )68. ( a 20 )( a 1) 89. a ( 2b n ) 269. ( x 7 )( x 8) 90. ( x 2 + 1)( x + 2 )( x 2 )70. ( x +10)( x 8) 91. ( a +1)( a 1) 271. ( m 16)( m 25) 92. 2a ( x 1) 272. ( 2 x 3 y ) 2 93. ( x + y )( x +1)( x 1)73. (1 a 3 )2 94. 2a( a + 4)( a 1)74. ( 4 + 5 x2 2 ) 95. 4 x( 2 x 3 y ) 275. (10 x 5 3a 4 y )6 2 96. ( 3 x y )( x + y )( x y )76. ab(3a + 6 5a b + 8ax + 4bm )2 97. 5a ( a + 1) ( a 2 a + 1)77. ( a +1)( a 1) 98. a ( 2 x +1)( 3 x 2 ) 2 278. 1 a 1 + a 99. ( m 2 + 9 )( n + 3)( n 3)4 4 3 379. ( 2a n b 2 n )( 2a n + b 2 n ) 100.2a ( 2 x +1)( 2 x 1)80. ( x 3 7 )( x 3 + 11) 101.ax( x + 5) 2 102.x ( x 7 )( x +1) x y 3 x y 3 81. + 2 9 2 9 ( m + 3)( m + 4)( m 4) 103.10 11. 104. ( x 2 y)3126.( a + 2b )( a 2b )( x + 2 y )105. ( a + b )( a b )( a + b 1)127. ( )(5a 2 3 x 2 + 2 3 x 2 2)106. ( 2ax 4a 2 3b ) 2128.( a + 4)( a 3) ( a 2 a + 12)107. ( x x 2 + 1 ( x 1) )129.( b 1)( x +1)( x 1)108. 4( x + 9 )( x 1)130.2 x 2 ( x + 7 )( x 4 )109. (a2 ) + a + 2 ( a 2 )( a + 1)5( 2a 5)( 3a + 2 )131.110. (x 3 + 2)( x 3) ( x 2 + 3x + 9 )132.( x y )( 3x 3 y 1)( 3x 3 y +1)111. ( a ( a + 1) a 4 a 3 + a 2 a + 1)133.a( x 3a )( 3a x ) ab( a + x + y )( a + x y )112.134. (a ( 4 5a ) 16 + 20a + 25a 2 )113. 3ab( m +1)( m 1)135.2 x 2 ( 7 x 3)( 5 x + 4 ) 3 xy ( 3 x + y ) (9 x 2 3 xy + y 2 )a 3 ( a 2 + 11)( a 2 5)114.136.115. ( a + 1)( a 1) ( a 2 a + 1)137. (ab 4a 2 7b 2) 2116. x( 3 x +1)(1 6 x )138. ()(x 2 7 x 2 3a 2 x 2 + 5a 2 )117. 2( 3a b )( x + b )139.x 2 ( x m y n )( x m + y n )118. am( m 4 )( m 3)140.( 2 x + 5)( x 3) ( x 2 + 3x + 9)119. ( 4a 2 ( x 1) x 2 + x + 1 )141.a ( x 2 ) ( x 2 + xy + y 2 )120. 7 xy ( 2 x + y )( 2 x y )142.121. 3ab( x 3)( x + 2 ) (x 2 ) + 2 xy + y 2 + 1 ( x + y + 1)( x + y 1)122. ( x + 4)( x 4) ( x 2 + 8)143.3a ( a 2 + a + 1)( a 2 a + 1)123. 2 y( 3x + 5 y ) 2144.(1 + a )(1 + a )(1 + a )(1 a ) 42124. ( a1)( x y ) 2 145.( a1)( a 1) ( a 2 a + 1)( a 2 + a + 1)125. x( x + 3 y )( x y )146.( x + 4)( x 4)( x + 5)( x 5) 11 12. 147. ( a + b) 2 ( a b) 2154. (x 4+ y 4 )( x 2 + y 2 )( x + y )( x y )148.( x( x + 1)( x 1) x 2 + 2 )155. ( x 2) ( x 2 + 2 x + 4)( x 1) ( x 2 x + 1)149. 2( x 1)( x + 3) ( x 2 + x + 1) 156. ( 2 + x ) ( 4 2 x + x 2 )( 2 x ) ( 4 + 2 x + x 2 )150.( ) 3 x 2 + 9 ( x + 3)( x 3) 157. ( a b ) 2 ( a + b ) ( a 2 + ab + b 2 )151. ( 2x + y) 2 ( 2x y) 2158. 2( 2 x + 1)( 2 x 1) ( x 2 + 1)152. x ( 3 x +1)( 3 x 1)( x + y )159. ( a + 3)( a 3)( a + 4)( a 4)153. 3a( 2 x + 1)( 2 x 1) ( x 2 + 3)160. a ( a + 2 )( x y ) ( x 2 + xy + y 2 )161. 12