Ejercicio 104

Comparte esto 👍👍
CAPITULO X

Descomposición Factorial
Ejercicio 104
Descomponer en 2 factores:
  1. 1+ (x+y ) 3 =[1+(x+y ) ] [1(x+y ) + (x+y ) 2 ] =(x+y+1 ) (1xy+ x 2 +2xy+ y 2 )
  2. 1 (a+b ) 3 =[1(a+b ) ] [1+(a+b ) + (a+b ) 2 ] =(1ab ) (1+a+b+ a 2 +2ab+ b 2 )
  3. 27+ (mn ) 3 =[3+(mn ) ] [ 3 2 3(mn ) + (mn ) 2 ] =(3+mn ) (93m+3n+ m 2 2mn+ n 2 )
  4. (xy ) 3 8 =[(xy ) 2 ] [ (xy ) 2 +2(xy ) +4 ] =(xy2 ) ( x 2 2xy+ y 2 +2x2y+4 )
  5. (x+2y ) 3 +1 =[(x+2y ) +1 ] [ (x+2y ) 2 (x+2y ) +1 ] =(x+2y+1 ) ( x 2 +4xy+4 y 2 x2y+1 )
  6. 1 (2ab ) 3 =[1(2ab ) ] [1+(2ab ) + (2ab ) 2 ] =(12a+b ) (1+2ab+4 a 2 4ab+ b 2 )
  7. a 3 + (a+1 ) 3 =[a+(a+1 ) ] [ a 2 a(a+1 ) + (a+1 ) 2 ] =(2a+1 ) ( a 2 a 2 a+ a 2 +2a+1 ) =(2a+1 ) ( a 2 a+1 )
  8. 8 a 3 (a1 ) 3 =[2a(a1 ) ] [ (2a ) 2 +2a(a1 ) + (a1 ) 2 ] =(2aa+1 ) (4 a 2 +2 a 2 2a+ a 2 2a+1 ) =(a+1 ) (7 a 2 4a+1 )
  9. 27 x 3 (xy ) 3 =[3x(xy ) ] [ (3x ) 2 +3x(xy ) + (xy ) 2 ] =(3xx+y ) (9 x 2 +3 x 2 3xy+ x 2 2xy+ y 2 ) =(2x+y ) (13 x 2 5xy+ y 2 )
  10. (2ab ) 3 27 =[(2ab ) 3 ] [ (2ab ) 2 +3(2ab ) + 3 2 ] =(2ab3 ) (4 a 2 4ab+ b 2 +6a3b+9 )
  11. x 6 (x+2 ) 3 =[ x 2 (x+2 ) ] [ ( x 2 ) 2 + x 2 (x+2 ) + (x+2 ) 2 ] =( x 2 x2 ) ( x 4 + x 4 +2 x 2 + x 2 +4x+4 ) =( x 2 x2 ) (2 x 4 +3 x 2 +4x+4 )
  12. (a+1 ) 3 + (a3 ) 3 =[(a+1 ) +(a3 ) ] [ (a+1 ) 2 (a+1 ) (a3 ) + (a3 ) 2 ] =(a+1+a3 ) [ a 2 +2a+1( a 2 2a3 ) + a 2 6a+9 ] =(2a2 ) [2 a 2 4a+10 a 2 +2a+3 ] =2(a1 ) ( a 2 2a+13 )
  13. (x1 ) 3 (x+2 ) 3 =[(x1 ) (x+2 ) ] [ (x1 ) 2 +(x1 ) (x+2 ) + (x+2 ) 2 ] =[ x 1 x 2 ] [ x 2 2x+1+ x 2 +x2+ x 2 +4x+4 ] =3(3 x 2 +3x+3 ) =9( x 2 +x+1 )
  14. (xy ) 3 (x+y ) 3 =[(xy ) (x+y ) ] [ (xy ) 2 +(xy ) (x+y ) + (x+y ) 2 ] =[ x y x y ] [ x 2 2xy + y 2 + x 2 y 2 + x 2 + 2xy + y 2 ] =2y(3 x 2 + y 2 )
  15. (m2 ) 3 + (m3 ) 3 =[(m2 ) +(m3 ) ] [ (m2 ) 2 (m2 ) (m3 ) + (m3 ) 2 ] =[m2+m3 ] [ m 2 4m+4( m 2 5m+6 ) + m 2 6m+9 ] =(2m5 ) [2 m 2 10m+13 m 2 +5m6 ] =(2m5 ) ( m 2 5m+7 )
  16. (2xy ) 3 + (3x+y ) 3 =[(2xy ) +(3x+y ) ] [ (2xy ) 2 (2xy ) (3x+y ) + (3x+y ) 2 ] =[2x y +3x+ y ] [4 x 2 4xy+ y 2 (6 x 2 xy y 2 ) +9 x 2 +6xy+ y 2 ] =5x[13 x 2 +2xy+2 y 2 6 x 2 +xy+ y 2 ] =5x(7 x 2 +3xy+3 y 2 )
  17. 8 (a+b ) 3 + (ab ) 3 =[2(a+b ) +(ab ) ] { [2(a+b ) ] 2 2(a+b ) (ab ) + (ab ) 2 } =[2a+2b+ab ] {4 (a+b ) 2 2( a 2 b 2 ) + a 2 2ab+ b 2 } =(3a+b ) {4( a 2 +2ab+ b 2 ) 2 a 2 +2 b 2 + a 2 2ab+ b 2 } =(3a+b ) {4 a 2 +8ab+4 b 2 a 2 +3 b 2 2ab } =(3a+b ) (3 a 2 +6ab+7 b 2 )
  18. 64 (m+n ) 3 125 =[4(m+n ) 5 ] { [4(m+n ) ] 2 +20(m+n ) + 5 2 } =[4m+4n5 ] {16 (m+n ) 2 +20m+20n+25 } =(4m+4n5 ) {16( m 2 +2mn+ n 2 ) +20m+20n+25 } =(4m+4n5 ) (16 m 2 +32mn+16 n 2 +20m+20n+25 )