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.

1. Multiply the first terms:
\(x \cdot x = x^2\)

2. Multiply the outer terms:
\(x \cdot (-3) = -3x\)

3. Multiply the inner terms:
\((-5) \cdot x = -5x\)

4. Multiply the last terms:
\((-5) \cdot (-3) = 15\)

Now, combine all these results:
\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

Thus, the fully expanded form of \((x - 5)(x - 3)\) is:
\[
x^2 - 8x + 15
\]

Now, we need to compare this with the given options:

A) \(3x^2 - 4x^2 - 3x - 15\)
B) \(2x - 2\)
C) \(x^2 - 8x + 15\)
D) \(x^2 - 2x + 15\)

The expression that matches our expansion \(x^2 - 8x + 15\) is option **C**.

So, the answer is **C** \(x^2 - 8x + 15\).