Show that (without expanding) $ \begin{vmatrix} 1 & x^2+yz & x^3 \\ 1 & y^2+zx & y^3 \\ 1 & z^2+xy & z^3 \end{vmatrix} = -(x-y) (y-z) (z-x) (x^2+y^2+z^2)$