Question

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 #

Answer 1

To determine the equivalence of Expression A \((x+4)(x−2)\) and Expression B \(x^2+2x−8\), we can proceed with the following steps:

First, let's simplify Expression A:

1. **Expression A: \((x+4)(x−2)\)**:
We can use the distributive property (also known as FOIL) to multiply the two terms:
\[
= x(x) + x(-2) + 4(x) + 4(-2)
\]
\[
= x^2 - 2x + 4x - 8
\]
\[
= x^2 + 2x - 8
\]

Now we can see that Expression A simplifies to \(x^2 + 2x - 8\), which matches Expression B.

Now we will match the options against our results:

1. **Option #1:** \((x+4)(x−2)\) - This is Expression A (Start).
2. **Option #2:** \(x^2−2x+4x−8\) - This is the step of expanding Expression A, which further simplifies to \(x^2 + 2x - 8\) but is not the final expression.
3. **Option #3:** \(x^2+2x−8\) - This is Expression B.
4. **Option #4:** \(x(x)−x(2)+4(x)−4(2)\) - This is another breakdown of Expression A when using the distributive property, quite similar to Option #2 but not simplified.

Let's summarize the matches:

- **First Option:** Option #1 \((x+4)(x−2)\)
- **Second Option:** Option #2 \(x^2−2x+4x−8\) (this shows a step in the expansion but isn't the final form).
- **Third Option:** Option #3 \(x^2 + 2x - 8\) (this is the equivalent expression).
- **Fourth Option:** Option #4 \(x(x)−x(2)+4(x)−4(2)\) (again this is a step showing the distributive property).

Putting it all together:

First: Option #1
Second: Option #2
Third: Option #3
Fourth: Option #4