因式分解:x²y-y²z+z²x-x²z+y²x+z²y-2xyz

分类: 作业答案 • 2022-02-02 09:31:08

问题描述：

因式分解:x²y-y²z+z²x-x²z+y²x+z²y-2xyz
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答

x²y-y²z+z²x-x²z+y²x+z²y-2xyz=y(x²-2xz+z²)+y²(x-z)-xz(x-z)=y(x-z)²+(y²-xz)(x-z)=(x-z)(xy-yz+y²-xz)=(x-z)[y(x+y)-z(x+y)]=(x-z)(x+y)(y-z)