Consider $a^{3}-b^{3}-a^{2}+b^{2}$ as a polynomial over variable $a$.
$$a^{3}-a^{2}-b^{3}+b^{2}$$
Find one factor of the form $a^{k}+m$, where $a^{k}$ divides the monomial with the highest power $a^{3}$ and $m$ divides the constant factor $-b^{3}+b^{2}$. One such factor is $a-b$. Factor the polynomial by dividing it by this factor.
