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
(4 points)
Expression 1 is equivalent to expression 2 because when we apply the distributive property to expression 1, we get 2x^2 - x^2 - 2x - 20 + 5.
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.