Question

Factorizar: (x+y+z)^3-(x+y-z)^3-(y+z-x)^3-(x+z-y)^3 Porfavor y paso a paso detallado, ojo:factorizar, gracias de antemano.

 

Saludos cordialerijillos :3

Answer 1

A= (x+y+z)³ = x³+(y+z)³+3x(y+z)(x+y+z)

 

-B= (x+y-z)³= -x³-(y-z)³-3x(y-z)(x+y-z)

 

-C= (y+z-x)³= -(y+z)³+x³+3(y+z)x(y+z-x)

 

-D=  (x-(y-z))³=-x³+(y-z)³+3x(y-z)(x-y+z)

 

los que estan en negrita se eliminan

 

3x(y+z)[x+y+z+y+z-x]+3x(y-z)[x-y+z-x-y+z]

3x(y+z)(2)(y+z)+3x(y-z)(2)(z-y)

6x(y+z)²-6x(y-z)²

6x[(y+z)²-(y-z)²]

6x(2y)(2z)

 

sol       24xyz

 

3x(y+z)(