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.