Question

From first to last, order the steps to prove that expression A is equivalent to expression B.

Expression A: (x+4)(x−2)


Expression B: x2+2x−8




Option #1: (x+4)(x−2)
(Start)

Option #2: x2−2x+4x−8


Option #3: x2+2x−8


Option #4: x(x)−x(2)+4(x)−4(2)


(2 points)
First: Option #

Second: Option #

Third: Option #

Fourth: Option #

Answer 1

To prove that Expression A, \((x+4)(x−2)\), is equivalent to Expression B, \(x^2 + 2x − 8\), we can follow these steps:

1. Start with Expression A: \( (x+4)(x−2) \) (Option #1).
2. Expand the expression using the distributive property:
\[ (x+4)(x−2) = x(x) - x(2) + 4(x) - 4(2) = x^2 - 2x + 4x - 8 \] (Option #4).
3. Combine like terms:
\[ x^2 - 2x + 4x - 8 = x^2 + 2x - 8 \] (Option #2).
4. You end up with Expression B: \( x^2 + 2x - 8 \) (Option #3).

So, the order of the steps is:

First: Option #1
Second: Option #4
Third: Option #2
Fourth: Option #3