Question

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

2x−2
2 x minus 2

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

x2−8x+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:

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

Calculating each term:

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

Now, combine all the terms:

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

Thus, \((x - 5)(x - 3)\) expands to:

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

Now, we can analyze the provided response options. The expression that we found, \(x^2 - 8x + 15\), matches with one of the responses given.

Therefore, the equivalent expression is:

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