Consider $x^{4}-5x^{2}y^{2}+4y^{4}$ as a polynomial over variable $x$.
$$x^{4}-5y^{2}x^{2}+4y^{4}$$
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 $4y^{4}$. One such factor is $x^{2}-4y^{2}$. Factor the polynomial by dividing it by this factor.
Consider $x^{2}-4y^{2}$. Rewrite $x^{2}-4y^{2}$ as $x^{2}-\left(2y\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(x-2y\right)\left(x+2y\right)$$
Consider $x^{2}-y^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
