Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3) .(1 point) Responses x2−2x+15 x squared minus 2 x plus 15 2x−2 2 x minus 2 x2−8x+15 x squared minus 8 x plus 15 3x2−4x2−3x−15

Answer 1

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:

\[ \boxed{x^2 - 8x + 15} \]