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

Question

Expression A: (x+4)(x−2)


Expression B: x^2+2x−8




Option #1: (x+4)(x−2) (Start)

Option #2: x^2−2x+4x−8


Option #3: x^2+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:

   • First: Option #1: \((x+4)(x−2)\) (Start)

2. Use the distributive property (also known as the FOIL method) to expand:

   • Second: Option #4: \(x(x)−x(2)+4(x)−4(2)\)

3. Simplify the expression:

   • Third: Option #2: \(x^2−2x+4x−8\)

4. Combine like terms:

   • Fourth: Option #3: \(x^2+2x−8\)

So, the correct order is:

First: Option #1

Second: Option #4

Third: Option #2

Fourth: Option #3