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

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

This simplifies to:

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

Combining like terms results in:

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

Now let's check the provided responses:

1. \(x^2 - 2x + 15\) - This is not equivalent to \(x^2 - 8x + 15\).
2. \(3x^2 - 4x^2 - 3x - 15\) - Simplifying this: \(3x^2 - 4x^2 = -x^2\), so this becomes \(-x^2 - 3x - 15\), which is not equivalent to \(x^2 - 8x + 15\).
3. \(2x - 2\) - This is also not equivalent to \(x^2 - 8x + 15\).

None of the given answers are correct. The equivalent expression to \((x-5)(x-3)\) through the Distributive Property is \(x^2 - 8x + 15\).