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 as follows:

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

Calculating each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \((-5) \cdot x = -5x\)
4. \((-5) \cdot (-3) = 15\)

Now combine these results:

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

Thus, the expression \((x - 5)(x - 3)\) simplifies to:

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

Now, comparing with the options given:

- \(3x^2 - 4x^2 - 3x - 15\) does not match.
- \(x^2 - 2x + 15\) does not match.
- \(2x - 2\) does not match.
- \(x^2 - 8x + 15\) matches.

Therefore, the expression equivalent to \((x - 5)(x - 3)\) is:

\[
\boxed{x^2 - 8x + 15}
\]