Question

From first to last, order the steps to prove that expression A is equivalent to expression B.%0D%0A%0D%0AExpression A: (x+4)(x−2)%0D%0A(%0D%0A𝑥%0D%0A+%0D%0A4%0D%0A)%0D%0A(%0D%0A𝑥%0D%0A−%0D%0A2%0D%0A)%0D%0A %0D%0A%0D%0AExpression B: x2+2x−8%0D%0A𝑥%0D%0A2%0D%0A+%0D%0A2%0D%0A𝑥%0D%0A−%0D%0A8%0D%0A %0D%0A%0D%0A %0D%0A%0D%0AOption #1: (x+4)(x−2)%0D%0A(%0D%0A𝑥%0D%0A+%0D%0A4%0D%0A)%0D%0A(%0D%0A𝑥%0D%0A−%0D%0A2%0D%0A)%0D%0A (Start)%0D%0A%0D%0AOption #2: x2−2x+4x−8%0D%0A𝑥%0D%0A2%0D%0A−%0D%0A2%0D%0A𝑥%0D%0A+%0D%0A4%0D%0A𝑥%0D%0A−%0D%0A8%0D%0A %0D%0A%0D%0AOption #3: x2+2x−8%0D%0A𝑥%0D%0A2%0D%0A+%0D%0A2%0D%0A𝑥%0D%0A−%0D%0A8%0D%0A %0D%0A%0D%0AOption #4: x(x)−x(2)+4(x)−4(2

Answer 1

To prove that Expression A is equivalent to Expression B, we can follow these steps in order:

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

2. **Expand Expression A using the distributive property**:
- This step involves distributing each term in the first parentheses to each term in the second parentheses using the FOIL method (First, Outer, Inner, Last):
- (x)(x) + (x)(-2) + (4)(x) + (4)(-2)

3. **Write out the expansion explicitly**:
x^2 - 2x + 4x - 8

4. **Combine like terms**:
(−2x + 4x) gives us 2x, so we combine it:
x^2 + 2x - 8

5. **Resulting in Expression B**:
x^2 + 2x - 8

Putting these steps together, the correct order is:

1. **Option #1**: (x + 4)(x - 2) (Start)
2. **Option #4**: x(x) - x(2) + 4(x) - 4(2)
3. **Option #2**: x^2 - 2x + 4x - 8
4. **Option #3**: x^2 + 2x - 8

Thus, the final ordered steps to prove that Expression A is equivalent to Expression B are: 1, 4, 2, 3.