Answer
$(x^2+4)(1+y)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
x^2+4+x^2y+4y
,$ 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 second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(x^2+4)+(x^2y+4y)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
(x^2+4)+y(x^2+4)
.\end{array}
Factoring the $GCF=
(x^2+4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x^2+4)(1+y)
.\end{array}