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

Question

Responses

x^2−8x+15

2x−2

x^2−2x+15

3x^2−4x^2−3x−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, distribute \(x\) and \(-5\):

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

Combine like terms:

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

Now, let's compare this result \(x^2 - 8x + 15\) with the given options:

1. \(x^2 - 8x + 15\) (This is correct).
2. \(2x - 2\) (Not correct).
3. \(x^2 - 2x + 15\) (Not correct).
4. \(3x^2 - 4x^2 - 3x - 15\) (This simplifies to \(-x^2 - 3x - 15\), also not correct).

The correct equivalent expression is:

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