Question

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

x2−8x+15
x squared minus 8 x plus 15

x2−2x+15
x squared minus 2 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 \((x−5)(x−3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression step by step:

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

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

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

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

5. **Combine all the results**:
\[
x^2 - 3x - 5x + 15
\]
Now combine the like terms:
\[
x^2 - 8x + 15
\]

Now we have expanded the expression \((x−5)(x−3)\) and found that it equals \(x^2 - 8x + 15\).

Now let's check the responses:

1. **\(x^2 - 8x + 15\)** (This matches our result.)
2. **\(x^2 - 2x + 15\)** (This does not match.)
3. **\(3x^2 - 4x^2 - 3x - 15\)** (This simplifies to \(-x^2 - 3x - 15\), which does not match.)
4. **\(2x - 2\)** (This does not match either.)

The correct expression equivalent to \((x−5)(x−3)\) is:

**\(x^2 - 8x + 15\)**