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

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 \((x−5)(x−3)\), we can use the Distributive Property (also known as the FOIL method for binomials).

1. **First:** Multiply the first terms:
\[
x \cdot x = x^2
\]

2. **Outer:** Multiply the outer terms:
\[
x \cdot (-3) = -3x
\]

3. **Inner:** Multiply the inner terms:
\[
-5 \cdot x = -5x
\]

4. **Last:** Multiply the last terms:
\[
-5 \cdot (-3) = 15
\]

Now, combine all these results:
\[
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
\]

So, the equivalent expression is:
\[
x^2 - 8x + 15
\]

Therefore, the correct response is:
**x² − 8x + 15.**