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

Answer 1

To prove that Expression 1 is equivalent to Expression 2 using the Distributive Property, we can expand Expression 1: (x-5)(x+3) = x(x) + x(3) -5(x) -5(3) = x^2 + 3x -5x -15 = 2x^2 -2x -15, which is equivalent to Expression 2 by combining like terms and rearranging them.