Question

Which of the following expression is equal to -3x^2-12?

Answer 1

$i=\sqrt{-1}\to i^2=-1\\\\-3x^2-12=-3(x^2+4)=-3(x^2+2^2)=-3(x^2-(-2^2))\\\\=-3(x^2-(-1\cdot2^2))=-3(x^2-(i^2\cdot2^2))=-3(x^2-(2i)^2)\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=-3(x-2i)(x+2i)\\\\\text{use distributive property}\\\\=\boxed{(-3x+6i)(x+2i)}\to\boxed{a.}$