Use the Distributive Property to verify which expression is equivalent to (x−5)(x−3) .(1 point)

Question

Responses

x^2−8x+15
x squared minus 8 x plus 15

3x^2−4x^2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15

x^2−2x+15
x squared minus 2 x plus 15

2x−2
2 x minus 2

Answer 1

To find the expression equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we can expand the expression as follows:

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

This gives us:

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

Combining like terms, we have:

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

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

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

Thus, the correct response from the options given is:

x^2−8x+15 (or x squared minus 8 x plus 15).