Answer
$5\sqrt{6}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(3\sqrt{2}+\sqrt{3})(2\sqrt{3}-\sqrt{2})
,$ use the FOIL method.
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
3\sqrt{2}(2\sqrt{3})+3\sqrt{2}(-\sqrt{2})+\sqrt{3}(2\sqrt{3})+\sqrt{3}(-\sqrt{2})
\\\\=
3(2)\sqrt{2(3)}-3\sqrt{2(2)}+2\sqrt{3(3)}-\sqrt{3(2)}
\\\\=
6\sqrt{6}-3\sqrt{4}+2\sqrt{9}-\sqrt{6}
\\\\=
6\sqrt{6}-3\sqrt{(2)^2}+2\sqrt{(3)^2}-\sqrt{6}
\\\\=
6\sqrt{6}-3(2)+2(3)-\sqrt{6}
\\\\=
6\sqrt{6}-6+6-\sqrt{6}
\\\\=
6\sqrt{6}-\sqrt{6}
\\\\=
5\sqrt{6}
.\end{array}
