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 x2−8x+15 x squared minus 8 x plus 15 3x2−4x2−3x−15 3 x squared minus 4 x squared minus 3 x minus 15 x2−2x+15

Answer 1

To verify which expression is equivalent to \((x - 5)(x - 3)\) using the Distributive Property, we need to expand the original expression.

We can apply the Distributive Property (also known as the FOIL method for binomials):

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

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 these results:

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

So, the expression \((x - 5)(x - 3)\) expands to:

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

Now, looking at the provided options, the equivalent expression is:

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