Factorize the following:

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

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

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

$=x y z(x+y+z)$