Question

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

x2−8x+15
x squared minus 8 x plus 15

2x−2
2 x minus 2

3x2−4x2−3x−15

Answer 1

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

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

Calculating \(x(x - 3)\):

\[
x^2 - 3x
\]

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

\[
-5x + 15
\]

Now, combine the two results:

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

Combine like terms:

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

Now we compare this result with the given options:

1. \(x^2 - 2x + 15\)
2. \(x^2 - 8x + 15\)
3. \(2x - 2\)
4. \(3x^2 - 4x^2 - 3x - 15\)

The expression we derived, \(x^2 - 8x + 15\), is equivalent to the second option:

**x^2 − 8x + 15**