因式分解：(x+y)的三次方+（z-x)的3次方-（y+z)的三次方
题目
因式分解：(x+y)的三次方+（z-x)的3次方-（y+z)的三次方
答案
(x+y)^3+(z-x)^3-(y+z)^3 =[(x+y)^3-(y+z)^3]+(z-x)^3 =[(x+y)-(y+z)][(x+y)^2+(x+y)(y+z)+(y+z)^2]+(z-x)^3 =(x-z)[(x+y)^2+(x+y)(y+z)+(y+z)^2]-(x-z)^3 =(x-z)[(x+y)^2+(x+y)(y+z)+(y+z)^2-(x-z)^2] =(x-z)[(x+y)^2+(x+y)(y+z)+(y+z+x-z)(y+z-x+z)] =(x-z)[(x+y)^2+(x+y)(y+z)+(x+y)(y+2z-x)] =(x-z)(x+y)[x+y+y+z+y+2z-x] =(x-z)(x+y)(3y+3z) =3(x+y)(y+z)(x-z)
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