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