e the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work. Expression 1:%C2%A0 (x−5)(x+3) Expression 2:%C2%A0 2x2−x2−2x−20+5

To prove that the two algebraic expressions \((x - 5)(x + 3)\) and \(2x^2 - x^2 - 2x - 20 + 5\) are equivalent using the Distributive Property, we'll expand Expression 1 and simplify Expression 2.

**Expression 1: \((x - 5)(x + 3)\)**
Using the Distributive Property (also known as the FOIL method for binomials), we distribute each term in the first binomial by each term in the second binomial:

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

**Expression 2: \(2x^2 - x^2 - 2x - 20 + 5\)**
Now, we simplify Expression 2 by combining like terms:

\[
2x^2 - x^2 = (2 - 1)x^2 = x^2
\]
\[
-2x
\]
\[
-20 + 5 = -15
\]
Thus, combining everything, we have:
\[
Expression 2 = x^2 - 2x - 15
\]

Now, since both Expression 1 and Expression 2 simplify to \(x^2 - 2x - 15\), we conclude that the two expressions are equivalent.

**Summary:**
Expression 1 simplifies to \(x^2 - 2x - 15\) via the Distributive Property. Expression 2 simplifies to \(x^2 - 2x - 15\) by combining like terms; therefore, both expressions are equivalent.