How do you factor completely  a+a^2b^2+a^3b^3?

$a + {a}^{2} {b}^{2} + {a}^{3} {b}^{3} = a \cdot \left(1 + a {b}^{2} + {a}^{2} {b}^{3}\right) = a \cdot \left(1 + a {b}^{2} \cdot \left(1 + a b\right)\right)$