#### Answer

$148$

#### Work Step by Step

Using $(a+b)(a-b)=a^2-b^2$, or the special product of the sum and difference of like terms, the given expression, $
(5\sqrt{6}-\sqrt{2})(5\sqrt{6}+\sqrt{2})
,$ simplifies to
\begin{array}{l}\require{cancel}
(5\sqrt{6})^2-(\sqrt{2})^2
\\\\=
25(6)-2
\\\\=
150-2
\\\\=
148
.\end{array}