Question

Which expression is equal to (x+2) (-x^2+2x-6)

A: -x^3-4x^2-2x-12
B: -x^3-4x^2-10x-12
C: -x^3-2x-12
D: -x^3-10x-12

Answer 1

`\huge\boxed{C.\ -x^3-2x-12}`

Explanation:

`(x+2)(-x^2+2x-6)\\\\=(x)(-x^2)+(x)(2x)+(x)(-6)+(2)(-x^2)+(2)(2x)+(2)(-6)\\\\=-x^3+2x^2-6x-2x^2+4x-12\\\\\text{combine like terms}\\\\=-x^3+(2x^2-2x^2)+(-6x+4x)-12\\\\=-x^3-2x-12`

Answer 2

In order to find out which expression is equal to (x+2) (-x^2+2x-6), we'll have to distribute this equation and simplify it. Here's how we do it:

Step 1: Distribute the inside of the parentheses (x+2) across each term within the other set of parentheses (-x^2+2x-6).

x*(-x^2) => -x^3 (Multiplying x with -x^2 gives -x^3)
x*(2x) => 2x^2 (Multiplying x with 2x gives 2x^2)
x*(-6) => -6x (Multiplying x with -6 gives -6x)

2*(-x^2) => -2x^2 (Multiplying 2 with -x^2 gives -2x^2)
2*(2x) => 4x (Multiplying 2 with 2x gives 4x)
2*(-6) => -12 (Multiplying 2 with -6 gives -12)

Step 2: Summing up all the terms to get the simplified expression:

- x^3 +2x^2 -6x -2x^2 +4x -12 = -x^3 -2x -12

So, the simplified expression is -x^3 -2x -12. Therefore, the correct answer is C: -x^3 -2x -12.