Answer
$(b+3)(x+y)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
3x+by+bx+3y
,$ such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3x+bx)+(by+3y)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
x(3+b)+y(b+3)
\\\\=
x(b+3)+y(b+3)
.\end{array}
Factoring the $GCF=
(b+3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(b+3)(x+y)
.\end{array}
