Answer
$(b+4-a)(b+4+a)$
Work Step by Step
The first $3$ terms of the given expression, $
b^2+8b+16-a^2
,$ is a perfect square trinomial. Hence, the factored form is
\begin{array}{l}\require{cancel}
(b^2+8b+16)-a^2
\\\\=
(b+4)^2-a^2
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of two squares, then the factored form of the expression, $
(b+4)^2-a^2
,$ is
\begin{array}{l}\require{cancel}
[(b+4)-a][(b+4)+a]
\\\\=
(b+4-a)(b+4+a)
.\end{array}
