Rewrite $a^{4}-16b^{4}$ as $\left(a^{2}\right)^{2}-\left(4b^{2}\right)^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$.
Consider $a^{2}-4b^{2}$. Rewrite $a^{2}-4b^{2}$ as $a^{2}-\left(2b\right)^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$.
