Consider $16m^{4}-65m^{2}n^{2}+49n^{4}$ as a polynomial over variable $m$.
$$16m^{4}-65n^{2}m^{2}+49n^{4}$$
Find one factor of the form $km^{p}+q$, where $km^{p}$ divides the monomial with the highest power $16m^{4}$ and $q$ divides the constant factor $49n^{4}$. One such factor is $16m^{2}-49n^{2}$. Factor the polynomial by dividing it by this factor.
Consider $16m^{2}-49n^{2}$. Rewrite $16m^{2}-49n^{2}$ as $\left(4m\right)^{2}-\left(7n\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
$$\left(4m-7n\right)\left(4m+7n\right)$$
Consider $m^{2}-n^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
