Answer
$(x+y)(x+7y)$
Work Step by Step
The given expression, $
x^2+7xy+6y^2
,$ has $c=
6
$ and $b=
7
.$
The possible factors of $c$ are $
\{ 1,6 \}
,\{ 2,3 \}
\{ -1,-6 \}
,\{ -2,-3 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
1,6
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+y)(x+7y)
.\end{array}
