Question

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.

Expression 1: (x−5)(x+3)


Expression 2: 2x2−x2−2x−20+5


(4 points)

Answer 1

could you say it more simply

Answer 2

To prove that the two expressions are equivalent using the Distributive Property, we'll expand Expression 1 and simplify Expression 2.

### Work for Expression 1:

1. **Expand (x−5)(x+3)** using the Distributive Property:
\[
(x - 5)(x + 3) = x(x + 3) - 5(x + 3)
\]
\[
= x^2 + 3x - 5x - 15
\]
\[
= x^2 - 2x - 15
\]

### Work for Expression 2:

2. **Simplify the Expression 2:**
\[
2x^2 - x^2 - 2x - 20 + 5
\]
- Combine like terms:
\[
= (2x^2 - x^2) - 2x - 20 + 5
\]
\[
= x^2 - 2x - 15
\]

### Conclusion:

Both expressions simplify to \(x^2 - 2x - 15\), therefore proving they are equivalent.

- Expression 1, when expanded, gives \(x^2 - 2x - 15\), and Expression 2 simplifies to the same form \(x^2 - 2x - 15\), confirming their equivalence.