Consider $x^{4}+y^{4}-2x^{2}y^{2}$ as a polynomial over variable $x$.
$$x^{4}-2y^{2}x^{2}+y^{4}$$
Find one factor of the form $x^{k}+m$, where $x^{k}$ divides the monomial with the highest power $x^{4}$ and $m$ divides the constant factor $y^{4}$. One such factor is $x^{2}-y^{2}$. Factor the polynomial by dividing it by this factor.
