Question

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

Answer 1

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

Using the Distributive Property (also known as the FOIL method for binomials), we have:

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

Now, calculating each part:

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

Now, we can combine these results:

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

So, \((x - 5)(x - 3) = x^2 - 8x + 15\).

Now we can compare this result with the provided options:

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

The equivalent expression is:

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