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To verify which expression is equivalent to \((x−5)(x−3)\) using the Distributive Property, we will expand the expression:
\[
(x−5)(x−3) = x \cdot x + x \cdot (-3) - 5 \cdot x - 5 \cdot (-3)
\]
Now perform the individual multiplications:
\[
= x^2 - 3x - 5x + 15
\]
Combine like terms:
\[
= x^2 - 8x + 15
\]
Now we will compare this result \(x^2 - 8x + 15\) with the given options:
1. \(x^2 - 2x + 15\)
2. \(3x^2 - 4x^2 - 3x - 15\) (which simplifies to \(-x^2 - 3x - 15\))
3. \(2x - 2\)
4. \(x^2 - 8x + 15\)
The correct equivalent expression to \((x−5)(x−3)\) is:
\[
\boxed{x^2 - 8x + 15}
\]