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