Answer
$-34-3\sqrt6$.
Work Step by Step
The given expression is
$=(2\sqrt3+5\sqrt2)(\sqrt3-4\sqrt2)$
Use FOIL method.
$=(2\sqrt3)(\sqrt3)+(2\sqrt3)(-4\sqrt2) +(5\sqrt2)(\sqrt3)+(5\sqrt2)(-4\sqrt2)$
Use product rule and simplify.
$=6-8\sqrt6 +5\sqrt6-40$
Add like terms.
$=-34-3\sqrt6$.
