Use the distributive property to prove that these algebraic expressions are equivalent. Explain the answer in 1 sentence.

Question

Expression 1:(x-5) (x+3)

Expression 2: 2x^2-x^2-2x-20+5

Answer 1

To prove that the expressions \((x-5)(x+3)\) and \(2x^2 - x^2 - 2x - 20 + 5\) are equivalent, we can expand Expression 1 using the distributive property:

\[ (x-5)(x+3) = x^2 + 3x - 5x - 15 = x^2 - 2x - 15. \]

Now, simplify Expression 2:

\[ 2x^2 - x^2 - 2x - 20 + 5 = x^2 - 2x - 15. \]

Since both expressions simplify to \(x^2 - 2x - 15\), they are equivalent.