Find the product . Simplify your answer. 3n^2(-2n^2+9) square

To find the product and simplify the expression \(3n^{2}(-2n^{2}+9)\), we need to distribute \(3n^{2}\) to each term inside the parentheses.<br /><br />First, distribute \(3n^{2}\) to \(-2n^{2}\):<br />\[<br />3n^{2} \cdot (-2n^{2}) = 3 \cdot (-2) \cdot n^{2} \cdot n^{2} = -6n^{4}<br />\]<br /><br />Next, distribute \(3n^{2}\) to \(9\):<br />\[<br />3n^{2} \cdot 9 = 3 \cdot 9 \cdot n^{2} = 27n^{2}<br />\]<br /><br />Now, combine these results:<br />\[<br />3n^{2}(-2n^{2} + 9) = -6n^{4} + 27n^{2}<br />\]<br /><br />Thus, the simplified answer is:<br />\[<br />\boxed{-6n^{4} + 27n^{2}}<br />\]