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Ejercicio 91

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DESCARGA
CAPITULO X

Descomposición Factorial
Ejercicio 91
Factorar o descomponer en dos factores:
  1. a 2 +ab+ax+bx =a( a+b ) +x( a+b ) =( a+b ) ( a+x )
  2. am–bm+an–bn =m( a–b ) +n( a–b ) =( a–b ) ( m+n )
  3. ax–2bx–2ay+4by =x( a–2b ) –2y( a–2b ) =( a–2b ) ( x–2y )
  4. a 2 x 2 –3b x 2 + a 2 y 2 –3b y 2 = x 2 ( a 2 –3b ) + y 2 ( a 2 –3b ) =( a 2 –3b ) ( x 2 + y 2 )
  5. 3m–2n–2n x 4 +3m x 4 =3m+3m x 4 –2n–2n x 4 =3m( 1+ x 4 ) –2n( 1+ x 4 ) =( 1+ x 4 ) ( 3m–2n )
  6. x 2 – a 2 +x– a 2 x = x 2 +x– a 2 x– a 2 =x( x+1 ) – a 2 ( x+1 ) =( x+1 ) ( x– a 2 )
  7. 4 a 3 –1– a 2 +4a =4a+4 a 3 –1– a 2 =4a( 1+ a 2 ) –( 1+ a 2 ) =( 1+ a 2 ) ( 4a–1 )
  8. x+ x 2 –x y 2 – y 2 =x+ x 2 – y 2 –x y 2 =x( 1+x ) – y 2 ( 1+x ) =( 1+x ) ( x– y 2 )
  9. 3ab x 2 –2 y 2 –2 x 2 +3ab y 2 =3ab x 2 +3ab y 2 –2 x 2 –2 y 2 =3ab( x 2 + y 2 ) –2( x 2 + y 2 ) =( x 2 + y 2 ) ( 3ab–2 )
  10. 3a– b 2 +2 b 2 x–6ax =3a–6ax– b 2 +2 b 2 x =3a( 1–2x ) – b 2 ( 1–2x ) =( 1–2x ) ( 3a– b 2 )
  11. 4 a 3 x–4 a 2 b+3bm–3amx =4 a 3 x–4 a 2 b–3amx+3bm =4 a 2 ( ax–b ) –3m( ax–b ) =( ax–b ) ( 4 a 2 –3m )
  12. 6ax+3a+1+2x =3a+6ax+( 1+2x ) =3a( 1+2x ) +( 1+2x ) =( 1+2x ) ( 3a+1 )
  13. 3 x 3 –9a x 2 –x+3a =3 x 2 ( x–3a ) –( x–3a ) =( x–3a ) ( 3 x 2 –1 )
  14. 2 a 2 x–5 a 2 y+15by–6bx =2 a 2 x–6bx–5 a 2 y+15by =2x( a 2 –3b ) –5y( a 2 –3b ) =( a 2 –3b ) ( 2x–5y )
  15. 2 x 2 y+2x z 2 + y 2 z 2 +x y 3 =2 x 2 y+2x z 2 +x y 3 + y 2 z 2 =2x( xy+ z 2 ) + y 2 ( xy+ z 2 ) =( xy+ z 2 ) ( 2x+ y 2 )
  16. 6m–9n+21nx–14mx =6m–9n–14mx+21nx =3( 2m–3n ) –7x( 2m–3n ) =( 2m–3n ) ( 3–7x )
  17. n 2 x–5 a 2 y 2 – n 2 y 2 +5 a 2 x = n 2 x– n 2 y 2 +5 a 2 x–5 a 2 y 2 = n 2 ( x– y 2 ) +5 a 2 ( x– y 2 ) =( x– y 2 ) ( n 2 +5 a 2 )
  18. 1+a+3ab+3b =1+a+3b+3ab =( 1+a ) +3b( 1+a ) =( 1+a ) ( 1+3b )
  19. 4a m 3 –12amn– m 2 +3n =4am( m 2 –3n ) –( m 2 –3n ) =( m 2 –3n ) ( 4am–1 )
  20. 20ax–5bx–2by+8ay =20ax–5bx+8ay–2by =5x( 4a–b ) +2y( 4a–b ) =( 4a–b ) ( 5x+2y )
  21. 3– x 2 +2ab x 2 –6ab =3– x 2 –6ab+2ab x 2 =( 3– x 2 ) –2ab( 3– x 2 ) =( 3– x 2 ) ( 1–2ab )
  22. a 3 + a 2 +a+1 = a 2 ( a+1 ) +( a+1 ) =( a+1 ) ( a 2 +1 )
  23. 3 a 2 –7 b 2 x+3ax–7a b 2 =3ax+3 a 2 –7 b 2 x–7a b 2 =3a( x+a ) –7 b 2 ( x+a ) =( x+a ) ( 3a–7 b 2 )
  24. 2am–2an+2a–m+n–1 =2a( m–n+1 ) –( m–n+1 ) =( m–n+1 ) ( 2a–1 )
  25. 3ax–2by–2bx–6a+3ay+4b =3ax+3ay–6a–2bx–2by+4b =3a( x+y–2 ) –2b( x+y–2 ) =( x+y–2 ) ( 3a–2b )
  26. a 3 +a+ a 2 +1+ x 2 + a 2 x 2 = a 3 +a+ a 2 +1+ a 2 x 2 + x 2 =a( a 2 +1 ) +( a 2 +1 ) + x 2 ( a 2 +1 ) =( a 2 +1 ) ( a+1+ x 2 )
  27. 3 a 3 –3 a 2 b+9a b 2 – a 2 +ab–3 b 2 =3a( a 2 –ab+3 b 2 ) –( a 2 –ab+3 b 2 ) =( a 2 –ab+3 b 2 ) ( 3a–1 )
  28. 2 x 3 –n x 2 +2x z 2 –n z 2 –3n y 2 +6x y 2 =2 x 3 +6x y 2 +2x z 2 –n x 2 –3n y 2 –n z 2 =2x( x 2 +3 y 2 + z 2 ) –n( x 2 +3 y 2 + z 2 ) =( x 2 +3 y 2 + z 2 ) ( 2x–n )
  29. 3 x 3 +2axy+2a y 2 –3x y 2 –2a x 2 –3 x 2 y =2axy+2a y 2 –2a x 2 –3 x 2 y–3x y 2 +3 x 3 =2a( xy+ y 2 – x 2 ) –3x( xy+ y 2 – x 2 ) =( xy+ y 2 – x 2 ) ( 2a–3x )
  30. a 2 b 3 – n 4 + a 2 b 3 x 2 – n 4 x 2 –3 a 2 b 3 x+3 n 4 x = a 2 b 3 –3 a 2 b 3 x+ a 2 b 3 x 2 – n 4 +3 n 4 x– n 4 x 2 = a 2 b 3 ( 1–3x+ x 2 ) – n 4 ( 1–3x+ x 2 ) =( 1–3x+ x 2 ) ( a 2 b 3 – n 4 )
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