#### Answer

$k-16m$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(\sqrt{k}+4\sqrt{m})(\sqrt{k}-4\sqrt{m})
,$ use the special product on multiplying the sum and difference of like terms.
$\bf{\text{Solution Details:}}$
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
(\sqrt{k})^2-(4\sqrt{m})^2
\\\\=
k-16m
.\end{array}