Factorize each of the following expressions:

$1+x+x y+x^{2} y$

$=(1+x)+\left(x y+x^{2} y\right)$           [Grouping the expressions]

$=(1+x)+x y(1+x)

$=(1+x y)(1+x)$         $[$ Taking $(1+x)$ as the common factor $]$