Answer
$-2\sqrt{7}$
Work Step by Step
Using the properties of radicals, the given expression, $
4\sqrt{63}-7\sqrt{28}
,$ simplifies to
\begin{array}{l}\require{cancel}
4\sqrt{9\cdot7}-7\sqrt{4\cdot7}
\\\\=
4\sqrt{(3)^2\cdot7}-7\sqrt{(2)^2\cdot7}
\\\\=
4\cdot3\sqrt{7}-7\cdot2\sqrt{7}
\\\\=
12\sqrt{7}-14\sqrt{7}
\\\\=
-2\sqrt{7}
.\end{array}
