Rewrite $81m^{4}-n^{4}$ as $\left(9m^{2}\right)^{2}-\left(n^{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
Consider $9m^{2}-n^{2}$. Rewrite $9m^{2}-n^{2}$ as $\left(3m\right)^{2}-n^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
