这道题怎么解：x²y-y²z+z²x-x²z+y²x+z²y-2xyz
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x2y-y2z+z2x-x2z+y2x+z2y-2xyz
解原式=x²y-y²z+z²x-x²z+y²x+z²y-2xyz
=x²y+y²x-xyz-y²z+yz²-xyz+z²x-x²z
=xy(x+y-z)-yz(x+y-z)+xz(z-x)
=(x+y-z)(xy-yz)+xz(z-x)
=y(x+y-z)(x-z)-xz(x-z)
=(x-z)(xy+y²-yz-xz)
=(x-z)[y(x+y)-z(x+y)]
=(x-z)(x+y)(y-z)
=(x+y)(x-z)(y-z)
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解原式=x²y-y²z+z²x-x²z+y²x+z²y-2xyz
=x²y+y²x-xyz-y²z+yz²-xyz+z²x-x²z
=xy(x+y-z)-yz(x+y-z)+xz(z-x)
=(x+y-z)(xy-yz)+xz(z-x)
=y(x+y-z)(x-z)-xz(x-z)
=(x-z)(xy+y²-yz-xz)
=(x-z)[y(x+y)-z(x+y)]
=(x-z)(x+y)(y-z)
=(x+y)(x-z)(y-z)
采纳给分儿。
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