Comparte esto 👍👍
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. ambm+anbn =m(ab ) +n(ab ) =(ab ) (m+n )
  3. ax2bx2ay+4by =x(a2b ) 2y(a2b ) =(a2b ) (x2y )
  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. 3m2n2n x 4 +3m x 4 =3m+3m x 4 2n2n x 4 =3m(1+ x 4 ) 2n(1+ x 4 ) =(1+ x 4 ) (3m2n )
  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 ) (4a1 )
  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 ) (3ab2 )
  10. 3a b 2 +2 b 2 x6ax =3a6ax b 2 +2 b 2 x =3a(12x ) b 2 (12x ) =(12x ) (3a b 2 )
  11. 4 a 3 x4 a 2 b+3bm3amx =4 a 3 x4 a 2 b3amx+3bm =4 a 2 (axb ) 3m(axb ) =(axb ) (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 (x3a ) (x3a ) =(x3a ) (3 x 2 1 )
  14. 2 a 2 x5 a 2 y+15by6bx =2 a 2 x6bx5 a 2 y+15by =2x( a 2 3b ) 5y( a 2 3b ) =( a 2 3b ) (2x5y )
  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. 6m9n+21nx14mx =6m9n14mx+21nx =3(2m3n ) 7x(2m3n ) =(2m3n ) (37x )
  17. n 2 x5 a 2 y 2 n 2 y 2 +5 a 2 x = n 2 x n 2 y 2 +5 a 2 x5 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 ) (4am1 )
  20. 20ax5bx2by+8ay =20ax5bx+8ay2by =5x(4ab ) +2y(4ab ) =(4ab ) (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 ) (12ab )
  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+3ax7a b 2 =3ax+3 a 2 7 b 2 x7a b 2 =3a(x+a ) 7 b 2 (x+a ) =(x+a ) (3a7 b 2 )
  24. 2am2an+2am+n1 =2a(mn+1 ) (mn+1 ) =(mn+1 ) (2a1 )
  25. 3ax2by2bx6a+3ay+4b =3ax+3ay6a2bx2by+4b =3a(x+y2 ) 2b(x+y2 ) =(x+y2 ) (3a2b )
  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 +ab3 b 2 =3a( a 2 ab+3 b 2 ) ( a 2 ab+3 b 2 ) =( a 2 ab+3 b 2 ) (3a1 )
  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 ) (2xn )
  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 y3x y 2 +3 x 3 =2a(xy+ y 2 x 2 ) 3x(xy+ y 2 x 2 ) =(xy+ y 2 x 2 ) (2a3x )
  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 (13x+ x 2 ) n 4 (13x+ x 2 ) =(13x+ x 2 ) ( a 2 b 3 n 4 )