Answer
$(a-b+4)^2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
(a-b)^2+8(a-b)+16
,$ simplify the expression using substitution. The resulting expression is a perfect square trinomial. Use the factoring of perfect square trinomials. Finally, substitute back the original expression.
$\bf{\text{Solution Details:}}$
Let $z=
(a-b)
.$ The given expression becomes
\begin{array}{l}\require{cancel}
z^2+8z+16
.\end{array}
The trinomial above is a perfect square trinomial. Using $a^2\pm2ab+b^2=(a\pm b)^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(z+4)^2
.\end{array}
Since $z=
(a-b)
,$, then the expression above becomes
\begin{array}{l}\require{cancel}
((a-b)+4)^2
\\\\
(a-b+4)^2
.\end{array}
