Question

分解因式（x+y+z）³+（3x-2y-3z）³-（4x-y-2x）³

两解，最好两解，要有过程，求高手。

Answer 1

(x+y+z)³+(3x-2y-3z)³-(4x-y-2z)³
=(x+y+z)³+[(3x-2y-3z)-(4x-y-2z)][(3x-2y-3z)²+(3x-2y-3z)(4x-y-2z)+(4x-y-2z)²]
=(x+y+z)³-(x+y+z)[(3x-2y-3z)²+(3x-2y-3z)(4x-y-2z)+(4x-y-2z)²]
=(x+y+z)[(x+y+z)²-(3x-2y-3z)²-(3x-2y-3z)(4x-y-2z)-(4x-y-2z)²]

追问

好像还能在分解。。。

Answer 2

设x+y+z=a,3x-2y-3z=b,那么4x-y-2z=a+b(题目肯定打错了)
a³+b³-(a+b)³
=a³+b³-(a³+b³+3a^2b+3ab^2)
=3ab(a+b)
=3(x+y+z)(3x-2y-3z)(4x-y-2z)

追问

没错，只要求分解因式

追答

我说错的是（4x-y-2x）³最后那个x是z,
还有我漏了个负号,最后是
=-3(x+y+z)(3x-2y-3z)(4x-y-2z)

追问

嗯，是打错了