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 two algebraic expressions are equivalent using the Distributive Property, we will first expand Expression 1 and then simplify Expression 2.

**Expression 1: (x - 5)(x + 3)**
Using the Distributive Property (also known as the FOIL method for binomials), we calculate:

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

**Expression 2: 2x^2 - x^2 - 2x - 20 + 5**
Now we simplify Expression 2 step by step:

\[
2x^2 - x^2 - 2x - 20 + 5
\]
First, combine like terms:

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

Now that both expressions have been simplified, we can see:

- Expression 1 simplifies to \(x^2 - 2x - 15\)
- Expression 2 simplifies to \(x^2 - 2x - 15\)

**Conclusion:** Since both expressions simplify to the same form \(x^2 - 2x - 15\), we have proved that the expressions \((x - 5)(x + 3)\) and \(2x^2 - x^2 - 2x - 20 + 5\) are equivalent.