Consider $4m^{8}-53m^{4}n^{4}+49n^{8}$ as a polynomial over variable $m$.
$$4m^{8}-53n^{4}m^{4}+49n^{8}$$
Find one factor of the form $km^{p}+q$, where $km^{p}$ divides the monomial with the highest power $4m^{8}$ and $q$ divides the constant factor $49n^{8}$. One such factor is $4m^{4}-49n^{4}$. Factor the polynomial by dividing it by this factor.
Consider $4m^{4}-49n^{4}$. Rewrite $4m^{4}-49n^{4}$ as $\left(2m^{2}\right)^{2}-\left(7n^{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
Consider $m^{4}-n^{4}$. Rewrite $m^{4}-n^{4}$ as $\left(m^{2}\right)^{2}-\left(n^{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.
