（x-y)³+（y-z)³+(z-x)³用立方和公示怎么因式分解
3个回答
（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-2z)(y-x)]
=(x-z)[(x-y)^2-(x-y)(y-z)-(x+y-2z)(x-y)]
=(x-z)(x-y)[(x-y)-(y-z)-(x+y-2z)]
=(x-z)(x-y)[x-y-y+z-(x+y-2z)]
=(x-z)(x-y)[x-2y+z-x-y+2z]
=(x-z)(x-y)[-2y+z-y+2z]
=(x-z)(x-y)(3z-3y)
=3(x-z)(x-y)(z-y)
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