Answer
$\color{blue}{-14+11\sqrt{10}}$
Work Step by Step
RECALL:
$(a+b)(c+d)=ac+ad+bc+bd$ (popularly known as the FOIL method)
Use the formula above to obtain:
$=(4\sqrt5)(3\sqrt2)+(4\sqrt5)(-\sqrt5)+(\sqrt2)(3\sqrt2)+(\sqrt2)(-\sqrt5)
\\=12\sqrt{10}-4(5)+3(2)-\sqrt{10}
\\=12\sqrt{10}-20+6-\sqrt{10}
\\=(12\sqrt{10}-\sqrt{10})+(-20+6)
\\=11\sqrt{10}+(-14)
\\=\color{blue}{-14+11\sqrt{10}}$
