Answer
$-7$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the expression $
\left( 3\sqrt{2}+5 \right)\left( 3\sqrt{2}-5 \right)
$ is equivalent to
\begin{array}{l}
\left( 3\sqrt{2} \right)^2-(5)^2
\\\\=
9\cdot2-25
\\\\=
18-25
\\\\=
-7
.\end{array}
