Answer
$(a^{2}+7b^{n})(a^{2}-7b^{n})$
Work Step by Step
Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the given expression, $
a^{2n}-49b^{2n}
,$ is
\begin{array}{l}
(a^{2}+7b^{n})(a^{2}-7b^{n})
\end{array}