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