Question

Use the Distributive Property to verify which expression is equivalent to (x - 5)(x - 3) point ) 2x - 2; x ^ 2 - 8x + 15; 3x ^ 2 - 4x ^ 2 - 3x - 15; x ^ 2 - 2x + 15

Answer 1

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

\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]
First, distribute \(x\) and \(-5\):

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

Combine like terms:

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

Now, we will evaluate the given options:

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

The expression that matches our expanded expression \(x^2 - 8x + 15\) is:

\[
\text{Option 2: } x^2 - 8x + 15
\]

Now let's check option 3:

\[
3x^2 - 4x^2 - 3x - 15 = (3x^2 - 4x^2) - 3x - 15 = -1x^2 - 3x - 15
\]

This does not match \(x^2 - 8x + 15\).

Options 1 and 4 do not match either, as both have different forms.

Thus, the expression that is equivalent to \((x - 5)(x - 3)\) is:

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