Answer
$2(x+4y)^2$
Work Step by Step
Factoring the $GCF=2$, then the given expression, $
2x^2+16xy+32y^2
$, is equivalent to $
2(x^2+8xy+16y^2)
$.\\
The two numbers whose product is $ac=
1(16)=16
$ and whose sum is $b=
8
$ are $\{
4,4
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2(x^2+8xy+16y^2)
$, is
\begin{array}{l}\require{cancel}
2(x^2+4xy+4xy+16y^2)
\\\\=
2[(x^2+4xy)+(4xy+16y^2)]
\\\\=
2[x(x+4y)+4y(x+4y)]
\\\\=
2[(x+4y)(x+4y)]
\\\\=
2(x+4y)^2
.\end{array}
