## Elementary Algebra

$51$
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}