Can anyone factorize this for me?
$\displaystyle x^4+y^4+z^4-2x^2y^2-2y^2z^2-2z^2x^2$.
Thanks.
Hint :
Solve $\displaystyle p(x,y,z)=0$ on $\displaystyle x^2$, its discriminant $\displaystyle \Delta=16y^2z^2$ is a perfect square, so you'll easily find the four roots $\displaystyle x_i=x_i(y,z)$ , hence $\displaystyle p(x,y,z)=\prod_{i=1}^4(x-x_i(y,z))$