Answer
$-16-3\sqrt{2}$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(2+3\sqrt{2})(1-3\sqrt{2})
,$ is equivalent to
\begin{align*}
&
2(1)+2(-3\sqrt{2})+3\sqrt{2}(1)+3\sqrt{2}(-3\sqrt{2})
\\&=
2-6\sqrt{2}+3\sqrt{2}-9(2)
\\&=
2-6\sqrt{2}+3\sqrt{2}-18
\\&=
(2-18)+(-6\sqrt{2}+3\sqrt{2})
\\&=
-16-3\sqrt{2}
.\end{align*}
Hence, the product of the given expression is $
-16-3\sqrt{2}
$.
