Question

Use the Distributive Property to verify which expression is equivalent to (x − 5) (x − 3).
A) 2x - 2
B) x^2 - 8x + 15
C) x^2 - 2x + 15
D) 3x^2 - 4x^2 - 3x - 15

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (also known as the FOIL method for binomials), we need to expand this expression.

1. Apply the Distributive Property (FOIL):
- First: \(x \cdot x = x^2\)
- Outside: \(x \cdot (-3) = -3x\)
- Inside: \(-5 \cdot x = -5x\)
- Last: \(-5 \cdot (-3) = 15\)

2. Combine the results:
\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

So, \((x - 5)(x - 3) = x^2 - 8x + 15\).

Now, let's compare this with the answer choices:

A) \(2x - 2\) → Not equivalent.

B) \(x^2 - 8x + 15\) → This is the correct equivalent expression.

C) \(x^2 - 2x + 15\) → Not equivalent.

D) \(3x^2 - 4x^2 - 3x - 15\) → This simplifies to \(-x^2 - 3x - 15\), which is not equivalent.

Therefore, the expression that is equivalent to \((x - 5)(x - 3)\) is **B) \(x^2 - 8x + 15\)**.