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)

Answer 1

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.