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)

(2 points)
First: Option #

Second: Option #

Third: Option #

Fourth: Option #

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Answer 1

To prove that expression A \((x+4)(x−2)\) is equivalent to expression B \(x^2+2x−8\), we can follow these ordered steps:

1. **First:** Option #1: \((x+4)(x−2)\) (Start)

2. **Second:** Option #2: \(x^2−2x+4x−8\) (Distributing the terms)

3. **Third:** Option #4: \(x(x)−x(2)+4(x)−4(2)\) (Breaking down the distribution)

4. **Fourth:** Option #3: \(x^2+2x−8\) (Combining like terms leads to Expression B)

So the final ordering would be:
- First: Option #1
- Second: Option #2
- Third: Option #4
- Fourth: Option #3