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

.(1 point)
Responses

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

2x−2
2 x minus 2

x2−8x+15

1 answer

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

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

Expanding this:

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

Now, combine the like terms:

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

So, \((x−5)(x−3)\) simplifies to \(x^2 - 8x + 15\).

Now, let's check the provided responses:

\(3x^2 - 4x^2 - 3x - 15\) simplifies to \(-x^2 - 3x - 15\) (not equivalent).
\(x^2 - 2x + 15\) (not equivalent).
\(2x - 2\) (not equivalent).
\(x^2 - 8x + 15\) (equivalent).

Thus, the correct expression is:

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