Question

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

3x^2−4x^2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15
x^2−8x+15
x squared minus 8 x plus 15
x^2−2x+15
x squared minus 2 x plus 15
2x−2
2 x minus 2

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 step by step.

1. Distribute the first terms:
\[
x \cdot x = x^2
\]

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

3. Distribute the inner terms:
\[
-5 \cdot x = -5x
\]

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

Now, we combine all these results:

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

Thus, \((x-5)(x-3)\) simplifies to \(x^2 - 8x + 15\).

Among the provided responses:
- The expression that matches this result is:
\[
x^2 - 8x + 15
\]
- The options are:
- \(x^2 - 8x + 15\)
- \(x^2 - 2x + 15\)
- \(2x - 2\)

Therefore, the correct answer is **\(x^2 - 8x + 15\)**.