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

Question

Responses

3x2−4x2−3x−15
3 x squared minus 4 x squared minus 3 x minus 15

x2−2x+15
x squared minus 2 x plus 15

2x−2
2 x minus 2

x2−8x+15

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we can expand the expression:

\[ (x - 5)(x - 3) = x(x - 3) - 5(x - 3) \]

Now, distributing \(x\) and \(-5\):

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

Combining like terms:

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

Now let's compare that result to the provided response options:

1. \(3x^2 - 4x^2 - 3x - 15\) (not a valid simplification)
2. \(x^2 - 2x + 15\) (not equivalent)
3. \(2x - 2\) (not equivalent)
4. \(x^2 - 8x + 15\) (this matches)

The correct equivalent expression is:

\[ \boxed{x^2 - 8x + 15} \]