Question

Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3) .(1 point) Responses
A. x^2 - 2x + 15
B. 3x^2 - 4x^2 - 3x - 15
C. x^2−8x+15
D. 2x−2

Answer 1

To verify which expression is equivalent to \((x−5)(x−3)\) using the Distributive Property, we can expand the expression:

\[
(x - 5)(x - 3) = x \cdot x + x \cdot (-3) - 5 \cdot x - 5 \cdot (-3)
\]

This simplifies as follows:

\[
= x^2 - 3x - 5x + 15
\]
\[
= x^2 - 8x + 15
\]

Now, we compare our result \(x^2 - 8x + 15\) with the provided options:

- A. \(x^2 - 2x + 15\) (not equivalent)
- B. \(3x^2 - 4x^2 - 3x - 15\) (not equivalent; simplifies to \(-x^2 - 3x - 15\))
- C. \(x^2 - 8x + 15\) (equivalent)
- D. \(2x - 2\) (not equivalent)

The correct answer is:

**C. \(x^2 - 8x + 15\)**