分解因式:(y-z)대+(z-x)대+(x-y)대. 要详细过程,谢谢

2025-05-14 03:26:14
推荐回答(1个)
回答1:

(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)