Rewrite $256x^{8}-y^{8}$ as $\left(16x^{4}\right)^{2}-\left(y^{4}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
Consider $16x^{4}-y^{4}$. Rewrite $16x^{4}-y^{4}$ as $\left(4x^{2}\right)^{2}-\left(y^{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
Consider $4x^{2}-y^{2}$. Rewrite $4x^{2}-y^{2}$ as $\left(2x\right)^{2}-y^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
