Find the product Simplify your answer. 3v(3v^2+2v+4) square

To find the product and simplify the expression \(3v(3v^2 + 2v + 4)\), we need to distribute \(3v\) to each term inside the parentheses.<br /><br />Let's break it down step by step:<br /><br />1. Distribute \(3v\) to \(3v^2\):<br /> \[<br /> 3v \cdot 3v^2 = 9v^3<br /> \]<br /><br />2. Distribute \(3v\) to \(2v\):<br /> \[<br /> 3v \cdot 2v = 6v^2<br /> \]<br /><br />3. Distribute \(3v\) to \(4\):<br /> \[<br /> 3v \cdot 4 = 12v<br /> \]<br /><br />Now, combine all these results:<br />\[<br />9v^3 + 6v^2 + 12v<br />\]<br /><br />So, the simplified form of the expression \(3v(3v^2 + 2v + 4)\) is:<br />\[<br />\boxed{9v^3 + 6v^2 + 12v}<br />\]