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: 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)

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 in the correct order:

1. Option #1: Start with the expression from Expression A: \((x + 4)(x - 2)\).

2. Option #4: Apply the distributive property (also known as the FOIL method for two binomials) to expand the expression:
   \[ x(x) - x(2) + 4(x) - 4(2) \]
   This leads to \(x^2 - 2x + 4x - 8\).

3. Option #2: Combine like terms:
   \[ x^2 - 2x + 4x - 8 = x^2 + 2x - 8 \]

4. Option #3: You arrive at Expression B:
   \[ x^2 + 2x - 8 \]

So the ordered steps are: Option #1, Option #4, Option #2, Option #3.