Question

Factorize:
a² + ab(b + 1) + b³

Answer 1

We have:
$a^2+ab\left(b+1\right)+b^3=a^2+a{b}^2+ab+b^3$
$$\begin{gathered} =\left(a^2+a{b}^2\right)+\left(ab+b^3\right) \\ =a\left(a+b^2\right)+b\left(a+b^2\right) \\ =\left(a+b^2\right)\left(a+b\right) \end{gathered}$$