Question

Question 1Using the Associative Property, which of the following expressions is equivalent to (4+17v)+4v(4+17𝑣)+4𝑣?(1 point)Responses21v2+421𝑣2+421 v squared plus 4(17v+4)+4v(17𝑣+4)+4𝑣open paren 17 v plus 4 close paren plus 4 v4+(17v+4v)

Answer 1

To solve for the expression equivalent to \((4 + 17v) + 4v\), we can apply the Associative Property of addition, which allows us to group terms differently.

1. The original expression is:
\[
(4 + 17v) + 4v
\]

2. According to the Associative Property:
\[
a + (b + c) = (a + b) + c
\]
Thus, we can rearrange the expression. In this case, we can rewrite it as:
\[
4 + (17v + 4v)
\]

3. Now, combine the like terms:
\[
17v + 4v = 21v
\]

4. Therefore, the expression simplifies to:
\[
4 + 21v
\]

Now, let's compare this result with the provided response options to identify the equivalent expression.

Based on your response options:
- \(21v^2 + 4\)
- \(21v^2 + 4\)
- \(4 + (17v + 4) + 4v(17v + 4) + 4v\)
- \(4 + (17v + 4v)\)

The expression \(4 + (17v + 4v)\) simplifies to \(4 + 21v\), which matches our result.

Thus, the expression equivalent to \((4 + 17v) + 4v\) is:

**Response: \(4 + (17v + 4v)\)**