Consider $m^{4}-1$. Rewrite $m^{4}-1$ as $\left(m^{2}\right)^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(m^{2}-1\right)\left(m^{2}+1\right)$$
Consider $m^{2}-1$. Rewrite $m^{2}-1$ as $m^{2}-1^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(m-1\right)\left(m+1\right)$$
Rewrite the complete factored expression. Polynomial $m^{2}+1$ is not factored since it does not have any rational roots.
