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

Question

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:

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