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.

Question

Expression 1: (x−5)(x+3)


Expression 2: 2x2−x2−2x−20+5


(4 points)

Answer 1

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.

Answer 2

could you say it more simply