Intermediate Algebra (12th Edition)

$k-16m$
$\bf{\text{Solution Outline:}}$ 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}