Rewrite $m^{4}-256$ as $\left(m^{2}\right)^{2}-16^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(m^{2}-16\right)\left(m^{2}+16\right)$$
Consider $m^{2}-16$. Rewrite $m^{2}-16$ as $m^{2}-4^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(m-4\right)\left(m+4\right)$$
Rewrite the complete factored expression. Polynomial $m^{2}+16$ is not factored since it does not have any rational roots.
