x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
=y(x^2-2xz+z^2)+(y^2x-y^2z)-(x^2x-z^2z)
=y(x-z)^2+y^2(x-z)-xz(x-z)
=(x-z)(xy-yz+y^2-xz)
=(x-z)[x(y-z)+y(y-z)]
=(x-z)(y-z)(x+y)