解: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)
