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

Answer 1

To verify which expression is equivalent to \((x−5)(x−3)\) using the Distributive Property, we can expand the expression:

\[ (x - 5)(x - 3) = x(x - 3) - 5(x - 3) \]

Expanding \(x(x - 3)\):

\[ x^2 - 3x \]

Expanding \(-5(x - 3)\):

\[ -5x + 15 \]

Now, combine the two results:

\[ x^2 - 3x - 5x + 15 \]

Combine like terms:

\[ x^2 - 8x + 15 \]

So, \((x - 5)(x - 3)\) is equivalent to:

\[ x^2 - 8x + 15 \]

Now looking at the responses, the correct answer is:

\(x^2 - 8x + 15\).