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