Answer
$(2x+3)(y+1)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
2xy+3y+2x+3
,$ such that the factored form of the groupings will result to a factor 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 second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2xy+3y)+(2x+3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
y(2x+3)+1(2x+3)
.\end{array}
Factoring the $GCF=
(2x+3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2x+3)(y+1)
.\end{array}