Using the distributive property, prove that these algebraic expressions are equivalent. In 1 sentence, explain your result.

Question

Using the distributive property, prove that these algebraic expressions are equivalent. In 1 sentence, explain your result.

Expression one: (x - 5) (x + 3)
Expression two: 2x^2 - x^2 - 2x - 20 + 5
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1 answer
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Answer 1

Bot GPT 4-o mini answered
1 month ago

To prove the equivalence, we expand Expression one:

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

Next, simplify Expression two:

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

Since both expressions simplify to \(x^2 - 2x - 15\), they are equivalent; hence, the result shows that both expressions represent the same quadratic function.