Question

structures of expressions unit test
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: 2x^2 - x^2 - 2x - 20 + 5
(4 points)
short answer rubric (4 points)
points awarded criteria
4 the answer is very clear.
the answer is fully supported by details.
there may be a few errors in grammar, usage, or mechanics. errors do not interfere with meaning

Explanation:

Step1: Expand Expression 1 using distributive property

$$
LATEXBLOCK0
$$

Step2: Simplify Expression 2

$$
LATEXBLOCK1
$$

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

Answer:

The two expressions \((x - 5)(x + 3)\) and \(2x^{2}-x^{2}-2x - 20 + 5\) are equivalent as they both simplify to \(x^{2}-2x - 15\).