Factorize the following:

The greatest common factor of the terms $a^{4} b, 3 a^{2} b^{2}$ and $6 a b^{3}$ of the expression $a^{4} b-3 a^{2} b^{2}-6 a b^{3}$ is $a b$.

Also, we can write $a^{4} b=a b \times a^{3}, 3 a^{2} b^{2}=a b \times 3 a b$ and $6 a b^{3}=a b \times 6 b^{2}$.

$\therefore a^{4} b-3 a^{2} b^{2}-6 a b^{3}=a b \times a^{3}-a b \times 3 a b-a b \times 6 b^{2}$

$=a b\left(a^{3}-3 a b-6 b^{2}\right)$