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:
- \(x \cdot x = x^2\)
- \(x \cdot (-3) = -3x\)
- \((-5) \cdot x = -5x\)
- \((-5) \cdot (-3) = 15\)
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:
\[ \boxed{x^2 - 8x + 15} \]