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To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we can expand the expression step by step.
Let's distribute:
\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]
Calculating \(x(x - 3)\):
\[
x^2 - 3x
\]
Now calculating \(-5(x - 3)\):
\[
-5x + 15
\]
Now, we can combine these results:
\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]
Thus, the expanded expression is:
\[
x^2 - 8x + 15
\]
Now, we can check the options provided:
1. \( x^2 - 2x + 15 \)
2. \( 2x - 2 \)
3. \( x^2 - 8x + 15 \) (This matches our result.)
4. \( 3x^2 - 4x^2 - 3x - 15 \)
The expression equivalent to \( (x - 5)(x - 3) \) is:
\[
\boxed{x^2 - 8x + 15}
\]