Answer
$4-2\sqrt{10}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, the given expression is equivalent to
$$\begin{aligned}
&
(3\sqrt{2})(4\sqrt{2})+(3\sqrt{2})(2\sqrt{5})-(2\sqrt{5})(4\sqrt{2})-(2\sqrt{5})(2\sqrt{5})
\\&=
12(2)+6\sqrt{10}-8\sqrt{10}-4(5)
\\&=
24+6\sqrt{10}-8\sqrt{10}-20
\\&=
4-2\sqrt{10}
.\end{aligned}
$$Hence, the given expression simplifies to $4-2\sqrt{10}$.
