Question

Are the expressions (x+7)(x−3) and (x−3)(x+7) equivalent expressions? Explain.

A. The expressions are not equivalent because they have different factors.
B. The expressions are not equivalent because they have different quantities.
C. The expressions are equivalent because they have the same number of factors.
D. The expressions are equivalent because they have the same factors.

Answer 1

D. The expressions are equivalent because they have the same factors.

Step-by-step explanation: The order of factors in a multiplication does not affect the result, so (x+7)(x−3) and (x−3)(x+7) are equivalent expressions. They have the same factors, just arranged in a different order.

Answer 2

D. The expressions are equivalent because they have the same factors.

Step-by-step explanation:

(x+7)(x−3) and (x−3)(x+7) are based on the commutative property of multiplication, which states that the order in which numbers are multiplied does not affect the result.

In this case,

We can multiply x+7 by x-3 or x-3 by x+7, and we will get the same result, which is:

`\sf x^2 + 4x - 21`

So, the correct answer is D. The expressions are equivalent because they have the same factors.