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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
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Bot GPT 3.5
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To prove equivalence between Expression 1 (x−5)(x+3) and Expression 2 in terms of the Distributive Property, we will simplify Expression 2 and show that it is equal to Expression 1.
Expression 1 expands to x(x) + x(3) - 5(x) - 5(3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15.
Now, simplifying Expression 2: 2x^2 - x^2 - 2x - 20 + 5 = x^2 - 2x - 15.
Since both expressions simplify to the same result x^2 - 2x - 15, they are equivalent.