Question

Помогите решить задачу!!! Скриншот ниже

Answer 1

$x^{2} (y-z)+y^{2}(z-x)+z^{2}(x-y)=x^{2}y-x^{2}z+y^{2} z-y^{2} x+z^{2}x-z^{2} y=\\\\=(x^{2}y-x^{2}z)+(y^{2}z-z^{2}y)+(z^{2}x-y^{2} x)=\\\\=x^{2}(y-z)+yz(y-z)+x(z-y)(z+y)= \\\\=x^{2}(y-z)+yz(y-z)-x(y-z)(z+y)=(y-z)(x^{2}+yz-xz-xy)=\\\\=(y-z)[(x^{2}-xy)+(yz-xz)]=(y-z)[(x^{2}-xy)-(xz-yz)] =\\\\=(y-z)[x(x-y)-z(x-y)]=\boxed{(y-z)(x-y)(x-z)}$