Consider $4x^{4}-9x^{2}y^{2}$. Factor out $x^{2}$.
$$x^{2}\left(4x^{2}-9y^{2}\right)$$
Consider $4x^{2}-9y^{2}$. Rewrite $4x^{2}-9y^{2}$ as $\left(2x\right)^{2}-\left(3y\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
