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 + 7) (x - 3)
Expression 2: 4x^2 - 3x^2 + 6x - 2x - 24 + 3

Keep your answer simple and as short as possible

Answer 1

(x+7)(x-3)=x(x-3)+7(x-3)=x^2-3x+7x-21=x^2+4x-21.

4x^2-3x^2+6x-2x-24+3=(4x^2-3x^2)+(6x-2x)+(-24+3)=x^2+4x-21.