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.