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

Expression 1:
(x − 5)(x + 3) = x(x + 3) − 5(x + 3) = x^2 + 3x − 5x − 15 = x^2 − 2x − 15.
One-sentence explanation: Using the distributive property (FOIL) we expanded (x − 5)(x + 3) to x^2 − 2x − 15.

Expression 2:
2x^2 − x^2 − 2x − 20 + 5 = (2x^2 − x^2) − 2x + (−20 + 5) = x^2 − 2x − 15.
One-sentence explanation: By combining like terms in 2x^2 − x^2 − 2x − 20 + 5 we simplify it to x^2 − 2x − 15.

Conclusion: Both expressions simplify to x^2 − 2x − 15, so they are equivalent.