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

2x−2
2 x minus 2

3x2−4x2−3x−15

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property (also known as the FOIL method for binomials), we can expand the expression:

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

Now, calculate each part:

1. \(x \cdot x = x^2\)
2. \(x \cdot (-3) = -3x\)
3. \(-5 \cdot x = -5x\)
4. \(-5 \cdot (-3) = 15\)

Now combine the terms:

\[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]

Thus, the expanded form of \((x - 5)(x - 3)\) is:

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

Comparing this with the given expressions, we find that the correct equivalent expression is:

x² - 8x + 15 (x squared minus 8 x plus 15).