Answer
$30+7\sqrt{15}$
Work Step by Step
Use the FOIL method, along with
$\sqrt{a}\times\sqrt{b}=\sqrt{ab},\qquad $
$\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a).
$F:\quad 3\sqrt{5}\times(4\sqrt{5})=3\times 4\times\sqrt{5\times 5}=12\times 5=60$
$O:\quad 3\sqrt{5}\times(5\sqrt{3})=3\times 5\times\sqrt{5\times 3}=15\sqrt{15}$
$I:\quad -2\sqrt{3}\times(4\sqrt{5})=-8\sqrt{3\times 5}=-8\sqrt{15}$
$L:\quad -2\sqrt{3}\times(5\sqrt{3})=-10\sqrt{3\times 3}=-10\times 3=-30$
Add like terms: (F+L)+(O+I)
$...$=$30+7\sqrt{15}$
