Question

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:

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