Answer
$12-2\sqrt{30}+2\sqrt{15}-5\sqrt{2}$
Work Step by Step
$(2\sqrt{3}+\sqrt{5})(2\sqrt{3}-\sqrt{10})=\qquad $... FOIL
$=(2\sqrt{3})(2\sqrt{3})-(2\sqrt{3})(\sqrt{10})+(\sqrt{5})(2\sqrt{3})-(\sqrt{5})(\sqrt{10})$
... $(\sqrt{3})^{2}=3,\qquad\sqrt{x}\sqrt{y}=\sqrt{xy}$
$=4\cdot 3-2\sqrt{30}+2\sqrt{15}-\sqrt{50}$
$=12-2\sqrt{30}+2\sqrt{15}-\sqrt{25\cdot 2}$
$=12-2\sqrt{30}+2\sqrt{15}-5\sqrt{2}$
