Factorize $2x+2y=2\bigl($
$\bigl)$
Factorize $ax+ay=a\bigl($
$\bigl)$
Factorize $2x+2y+ax+ay=2\bigl($
$\bigl)+a\bigl($
$\bigl)$
$\phantom{Factorize 2x+2y+ax+a}=\bigl(\textcolor{red}{x+y}\bigl)\bigl($
$\bigl)$
Factorize $x^2+3x+xy+3y$
$\phantom{Facto}=x\bigl($
$\bigl)+y\bigl($
$\bigl)$
$\phantom{Facto}=\bigl(x+3\bigl)\bigl($
$\bigl)$
Factorize $ab+b^2-3a-3b$
$\phantom{Facto}=$
$\bigl($
$\bigl)-3\bigl($
$\bigl)$
$\phantom{Facto}=\bigl(a+b\bigl)\bigl($
$\bigl)$
Factorize $5x+3y+xy+15$
This can be rearranged to:
$=5x+xy+3y+15$
$=x\bigl($
$\bigl)+$
$\bigl($
$\bigl)$
$=$
$=5x+15+xy+3y$
$=5\bigl($
$\bigl)+$
$\bigl($
$\bigl)$
$=$