Answer
$2(a-4)^2$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression, $
2a^2-16a+32
,$ is equivalent to
\begin{align*}
2(a^2-8a+16)
.\end{align*}
Using $(x\pm y)^2=(x)^2\pm2(x\cdot y)+(y)^2$ or the square of a binomial, the factored form of the expression above is
\begin{align*}
&
2[(a)^2-2(4a)+(4)^2]
\\&=
2[(a)^2-2(a\cdot4)+(4)^2]
\\&=
2[(a-4)^2]
\\&=
2(a-4)^2
.\end{align*}
