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

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