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 as follows:
\[ = x^2 - 3x - 5x + 15 \] \[ = x^2 - 8x + 15 \]
Now, we compare our result \(x^2 - 8x + 15\) with the provided options:
- A. \(x^2 - 2x + 15\) (not equivalent)
- B. \(3x^2 - 4x^2 - 3x - 15\) (not equivalent; simplifies to \(-x^2 - 3x - 15\))
- C. \(x^2 - 8x + 15\) (equivalent)
- D. \(2x - 2\) (not equivalent)
The correct answer is:
C. \(x^2 - 8x + 15\)