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

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