Consider $99a^{2}-202ab+99b^{2}$ as a polynomial over variable $a$.
$$99a^{2}-202ba+99b^{2}$$
Find one factor of the form $ka^{m}+n$, where $ka^{m}$ divides the monomial with the highest power $99a^{2}$ and $n$ divides the constant factor $99b^{2}$. One such factor is $9a-11b$. Factor the polynomial by dividing it by this factor.