Rewrite $a^{8}-b^{8}$ as $\left(a^{4}\right)^{2}-\left(b^{4}\right)^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$.
Consider $a^{4}-b^{4}$. Rewrite $a^{4}-b^{4}$ as $\left(a^{2}\right)^{2}-\left(b^{2}\right)^{2}$. The difference of squares can be factored using the rule: $p^{2}-q^{2}=\left(p-q\right)\left(p+q\right)$.
