因式分解：x²y-y²z+z²x-x²z+y²x+z²y-2xyz

因式分解：x²y-y²z+z²x-x²z+y²x+z²y-2xyz
因式分解：x²y-y²z+z²x-x²z+y²x+z²y-2xyz

因式分解：x²y-y²z+z²x-x²z+y²x+z²y-2xyz
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)