Answer
$16m^{2}-49n^{4}$
Work Step by Step
From Page 301, we know that the product of a sum and difference of two terms $x$ and $y$ is given by the following equation: $(x+y)(x-y)=x^{2}-y^{2}$.
Therefore, $(4m+7n^{2})(4m-7n^{2})=(4m)^{2}-(7n^{2})^{2}=4^{2}m^{2}-7^{2}(n^{2})^{2}=16m^{2}-49n^{4}$.