Ask a New Question
Menu

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)

1 answer

To prove that expression A is equivalent to expression B, we will first expand expression A step by step. Here are the ordered steps to do so:

  1. Option #1: Start with expression A: \((x+4)(x−2)\).

  2. Option #4: Use the distributive property (FOIL) to expand: \[ x(x) - x(2) + 4(x) - 4(2) \implies x^2 - 2x + 4x - 8. \]

  3. Option #2: Combine like terms from the previous step: \[ x^2 - 2x + 4x - 8 \implies x^2 + 2x - 8. \]

  4. Option #3: Resulting in expression B: \(x^2 + 2x - 8\).

So the correct order from first to last is: 1 -> 4 -> 2 -> 3.