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)

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 in order:

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

2. **Second:** Expand the expression using the distributive property:
- **Option #4:** \(x(x)−x(2)+4(x)−4(2)\)

3. **Third:** Combine like terms from the expansion:
- **Option #2:** \(x^2−2x+4x−8\) (which simplifies to \(x^2 + 2x - 8\))

4. **Fourth:** This confirms that the expanded form is equivalent to expression B:
- **Option #3:** \(x^2 + 2x - 8\)

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