Consider $512-a^{3}b^{9}$ as a polynomial over variable $a$.
$$-b^{9}a^{3}+512$$
Find one factor of the form $kb^{m}a^{n}+p$, where $kb^{m}a^{n}$ divides the monomial with the highest power $-b^{9}a^{3}$ and $p$ divides the constant factor $512$. One such factor is $ab^{3}-8$. Factor the polynomial by dividing it by this factor.
