Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work.

To prove that the expressions \((x−5)(x+3)\) and \(2x^2−x^2−2x−20+5\) are equivalent, we will first simplify Expression 1 using the Distributive Property:

\[
(x−5)(x+3) = x(x+3) - 5(x+3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15.
\]

Next, we will simplify Expression 2:

\[
2x^2 - x^2 - 2x - 20 + 5 = (2x^2 - x^2) - 2x - 20 + 5 = x^2 - 2x - 15.
\]

Since both expressions simplify to \(x^2 - 2x - 15\), we can conclude that they are equivalent.