Answer
$(x+2y)(x+4y)$
Work Step by Step
The given expression, $
x^2+6xy+8y^2
,$ has $c=
8
$ and $b=
6
.$
The possible factors of $c$ are $
\{ 1,8 \}
,\{ 2,4 \}
\{ -1,-8 \}
,\{ -2,-4 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
2,4
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+2y)(x+4y)
.\end{array}