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

Question

x2−2x+15

3x2−4x2−3x−15

2x−2

x2−8x+15

Answer 1

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

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

Now perform the individual multiplications:

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

Combine like terms:

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

Now we will compare this result \(x^2 - 8x + 15\) with the given options:

1. \(x^2 - 2x + 15\)
2. \(3x^2 - 4x^2 - 3x - 15\) (which simplifies to \(-x^2 - 3x - 15\))
3. \(2x - 2\)
4. \(x^2 - 8x + 15\)

The correct equivalent expression to \((x−5)(x−3)\) is:

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