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:
- 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:
- Option #1: \((x+4)(x−2)\) - This is Expression A (Start).
- 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.
- Option #3: \(x^2+2x−8\) - This is Expression B.
- 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
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