## Precalculus (6th Edition)

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