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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 to:
\[
x^2 - 3x - 5x + 15
\]
Combining like terms results in:
\[
x^2 - 8x + 15
\]
Now let's check the provided responses:
1. \(x^2 - 2x + 15\) - This is not equivalent to \(x^2 - 8x + 15\).
2. \(3x^2 - 4x^2 - 3x - 15\) - Simplifying this: \(3x^2 - 4x^2 = -x^2\), so this becomes \(-x^2 - 3x - 15\), which is not equivalent to \(x^2 - 8x + 15\).
3. \(2x - 2\) - This is also not equivalent to \(x^2 - 8x + 15\).
None of the given answers are correct. The equivalent expression to \((x-5)(x-3)\) through the Distributive Property is \(x^2 - 8x + 15\).