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To determine which expression is equivalent to \((4 + 17v) + 4v\) using the Associative Property, we can apply the property, which states that the way numbers are grouped in addition does not change their sum.
Starting with the given expression:
\[
(4 + 17v) + 4v
\]
According to the Associative Property, we can regroup the terms:
\[
4 + (17v + 4v)
\]
This shows how the expression can be rewritten by changing the grouping of the terms.
Now, let's check the options provided:
1. \(21v^2 + 4\)
2. \((17v + 4) + 4v\)
3. \(4 + (17v + 4v)\)
Among these, the expression \(4 + (17v + 4v)\) is a direct result of applying the Associative Property to the original expression.
Thus, the correct answer is:
\[
4 + (17v + 4v)
\]