Question

From first to last, order the steps to prove that expression A is equivalent to expression B. Expression A: (x+4)(x−2)(x+4)(x−2) Expression B: x2+2x−8x2+2x−8 Option #1: (x+4)(x−2)(x+4)(x−2) (Start) Option #2: x2−2x+4x−8x2−2x+4x−8 Option #3: x2+2x−8x2+2x−8 Option #4: x(x)−x(2)+4(x)−4(2)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 is equivalent to Expression B, we need to follow logical steps to simplify Expression A, and then show that it can be transformed into Expression B. Here’s how the steps would go in order:

1. **First:** Start with Option #1: **(x + 4)(x - 2)(x + 4)(x - 2)** (Expression A)

2. **Second:** Expand the expression using the distributive property (FOIL method) on the first two factors:
- Option #4: **x(x) - x(2) + 4(x) - 4(2)** (this step is equivalent to expanding (x+4)(x-2))

3. **Third:** After expanding, combine like terms. You would see something like:
- Option #2: **x^2 - 2x + 4x - 8** (this is after expanding and combining)

4. **Fourth:** Finally, combine like terms to get to Expression B:
- Option #3: **x^2 + 2x - 8** (which is Expression B)

The complete order is:
- First: Option #1
- Second: Option #4
- Third: Option #2
- Fourth: Option #3