Factorize the following:

The greatest common factor of the terms ax $^{2} y, b x y^{2}$ and cxyz of the expression ax $^{2} y+b x y^{2}+c x y z$ is $x y$.

Also, we can write $a x^{2} y=x y \times a x, b x y^{2}=x y \times b y$ and $c x y z=x y \times c z$.

$\therefore a x^{2} y+b x y^{2}+c x y z=x y \times a x+x y \times b y+x y \times c z$

$=x y(a x+b y+c z)$