#### Answer

$51$

#### 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{3}+2\sqrt{6})(5\sqrt{3}-2\sqrt{6})
,$ simplifies to
\begin{array}{l}\require{cancel}
(5\sqrt{3})^2-(2\sqrt{6})^2
\\\\=
25(3)-4(6)
\\\\=
75-24
\\\\=
51
.\end{array}