分解因式：（y-z）³+（z-x）³+（x-y）³. 要详细过程，谢谢
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（y-z）³+（z-x）³+（x-y）³
=（y-z+z-x）[(y-z)²+(y-z)(z-x)+(z-x)²] -(y-x)³
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x)²] -(y-x)³
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x)²-(y-x)²]
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x+y-x)(z-x-y+x)]
=(y-x)[(y-z)²+(y-z)(z-x)+(z+y-2x)(z-y)]
=(y-x)[(y-z)(y-z+z-x-z-y+2x)]
=(y-x)(y-z)(x-z)
=（y-z+z-x）[(y-z)²+(y-z)(z-x)+(z-x)²] -(y-x)³
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x)²] -(y-x)³
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x)²-(y-x)²]
=(y-x)[(y-z)²+(y-z)(z-x)+(z-x+y-x)(z-x-y+x)]
=(y-x)[(y-z)²+(y-z)(z-x)+(z+y-2x)(z-y)]
=(y-x)[(y-z)(y-z+z-x-z-y+2x)]
=(y-x)(y-z)(x-z)
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