Do the grouping $ab^{2}-bc^{2}-ab+c^{2}=\left(ab^{2}-bc^{2}\right)+\left(-ab+c^{2}\right)$, and factor out $b$ in the first and $-1$ in the second group.
$$b\left(ab-c^{2}\right)-\left(ab-c^{2}\right)$$
Factor out common term $ab-c^{2}$ by using distributive property.
