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:   4x2 + 3x2 +6x − 2x −24 + 3

1 answer

Expression 1: (x + 7)(x - 3) is equivalent to x(x - 3) + 7(x - 3) by using the Distributive Property.

Expression 2: 4x^2 + 3x^2 + 6x - 2x - 24 + 3 is equivalent to 7x^2 + 4x - 21 by combining like terms.
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