Question

Factorize:
a³ + ab(1 − 2a) − 2b²

Answer 1

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