Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3).(1 point)

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

Using the FOIL method:

1. **First**: Multiply the first terms: \(x \cdot x = x^2\)
2. **Outside**: Multiply the outside terms: \(x \cdot (-3) = -3x\)
3. **Inside**: Multiply the inside terms: \(-5 \cdot x = -5x\)
4. **Last**: Multiply the last terms: \(-5 \cdot (-3) = 15\)

Now combine all these results:

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

Combine the like terms:

\[
x^2 - 8x + 15
\]

So, the expression \((x-5)(x-3)\) simplifies to \(x^2 - 8x + 15\).

Now let's compare this with the provided responses:

- \(x^2 - 2x + 15\) (not equivalent)
- **\(x^2 - 8x + 15\)** (this matches)
- \(2x - 2\) (not equivalent)
- \(3x^2 - 4x^2 - 3x - 15\) (this does not simplify to the correct form)

Thus, the correct answer is:

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