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 - no response given

2x−2
2 x minus 2 - no response given

3x2−4x2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15 - incorrect

x2−8x+15

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression as follows:

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

Calculating each term:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \(-5 \cdot x = -5x\)
4. \(-5 \cdot (-3) = 15\)

Now combine all these terms:

\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

So, the expression we derived from \((x - 5)(x - 3)\) is:

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

Now, comparing this with the given expressions, the equivalent expression is:

\[
\text{Answer: } x^2 - 8x + 15
\]

Thus, the correct response is:

**x² - 8x + 15**.