Answer
$-14+11\sqrt{10}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(4\sqrt{5}+\sqrt{2})(3\sqrt{2}-\sqrt{5})
,$ 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}
4\sqrt{5}(3\sqrt{2})+4\sqrt{5}(-\sqrt{5})+\sqrt{2}(3\sqrt{2})+\sqrt{2}(-\sqrt{5})
\\\\=
4(3)\sqrt{5(2)}-4\sqrt{5(5)}+3\sqrt{2(2)}-\sqrt{2(5)}
\\\\=
12\sqrt{10}-4\sqrt{(5)^2}+3\sqrt{(2)^2}-\sqrt{10}
\\\\=
12\sqrt{10}-4(5)+3(2)-\sqrt{10}
\\\\=
12\sqrt{10}-20+6-\sqrt{10}
\\\\=
(-20+6)+(12\sqrt{10}-\sqrt{10})
\\\\=
-14+11\sqrt{10}
.\end{array}
