Question

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

A. (-3x+2i)(x-6i)
B. (-3x-6i)(x+2i)
C.(-3x+6i)(x+2i)
D. (-3x-4i)(x-3i)

Answer 1

Given expression:
`-3x^2-12.`

Let us factor out Greatest Common Factor first.

Greatest Common Factor is -3 there.

Factoring out -3 there.

`-3(x^2+4)`

4 could be written as
`-(2i)^2`.

Therefore,

`-3(x^2+4) = -3[x^2-(2i)^2]`

Applying difference of the square identity
`(a)^2-(b)^2 = (a-b)(a+b)`, we get

`-3[x^2-(2i)^2] = -3(x-2i)(x+2i)`

Distributing -3 in first parenthesis, we get

-3(x-2i)(x+2i) = (-3x+6i)(x+2i)

Therefore, correct option is C.(-3x+6i)(x+2i).