因式分解x的平方（y-z）+y的平方（z-x）+z的平方（x-y）

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