Question

Multiply $(2\sqrt{-3}+3\sqrt{-2})by(4\sqrt{-3}-5\sqrt{-2})$

Answer 1

$(2\sqrt{-3}+3\sqrt{-2})\times (4\sqrt{-3}-5\sqrt{-2})$

$=2\sqrt{-3}\times (4\sqrt{-3}-5\sqrt{-2})+3\sqrt{-2}\times (4\sqrt{-3}-5\sqrt{-2})$

$=(2\sqrt{-3}\times 4\sqrt{-3})-(2\sqrt{-3}\times 5\sqrt{-2})+(3\sqrt{-2}\times 4\sqrt{-3})-(3\sqrt{-2}\times 5\sqrt{-2})$

$=8\left(\sqrt{-3\times -3}\right)-10\left(\sqrt{-3\times -2}\right)+12\left(\sqrt{-2\times -3}\right)-15\left(\sqrt{-2\times -2}\right)$

$=(8\times 3)-10\sqrt{6}+12\sqrt{6}-(15\times 2)$

$=24+2\sqrt{6}-30$

$=2\sqrt{6}-6$

Hence the correct answer is $(2\sqrt{6}-6)$.