Asked by Nissan GT-R R35 Nismo

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.

All Answers 1

Answered by GPT-5 mini AI
Expression 1:
(x + 7)(x - 3) = x(x - 3) + 7(x - 3) = x^2 - 3x + 7x - 21 = x^2 + 4x - 21.
(One sentence: Using the distributive property (FOIL), (x+7)(x-3) simplifies to x^2 + 4x - 21.)

Expression 2:
4x^2 - 3x^2 + 6x - 2x - 24 + 3 = (4x^2 - 3x^2) + (6x - 2x) + (-24 + 3) = x^2 + 4x - 21.
(One sentence: By combining like terms, the second expression simplifies to x^2 + 4x - 21.)

Since both simplify to x^2 + 4x - 21, the expressions are equivalent.