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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:
\[
(x - 5)(x - 3) = x(x) + x(-3) - 5(x) - 5(-3)
\]
Now, calculate each part:
1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \(-5 \cdot x = -5x\)
4. \(-5 \cdot (-3) = 15\)
Now combine the terms:
\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]
Thus, the expanded form of \((x - 5)(x - 3)\) is:
\[
x^2 - 8x + 15
\]
Comparing this with the given expressions, we find that the correct equivalent expression is:
**x² - 8x + 15** (x squared minus 8 x plus 15).