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

Question

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.