Question

33 PIONTS! 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

Answer 1

Sure, let's use the Distributive Property to prove that these algebraic expressions are equivalent.

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

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

Explanation for Expression 1:

In Expression 1, we apply the Distributive Property by multiplying each term in the first set of parentheses (x) by each term in the second set of parentheses (x and 3) and then adding the results.

(x - 5)(x + 3) = x(x) + x(3) - 5(x) - 5(3)

Now, simplify each term:

x^2 + 3x - 5x - 15

Combine like terms:

x^2 - 2x - 15

Explanation for Expression 2:

In Expression 2, we simplify the expression by first combining like terms and then applying the Distributive Property.

2x^2 - x^2 - 2x - 20 + 5 = (2 - 1)x^2 - 2x - 20 + 5

Now, apply the Distributive Property:

x^2 - 2x - 20 + 5

Combine like terms:

x^2 - 2x - 15

As you can see, both expressions simplify to x^2 - 2x - 15, demonstrating that they are equivalent.