Find the product. \( x(4 x+3)^{2} \) \( \begin{array}{l}x(4 x+3)^{2}=\square \\ (\text { Simplify your answer. })\end{array} \)

To find the product \( x(4x + 3)^{2} \), we first expand \( (4x + 3)^{2} \). Using the formula \( (a + b)^{2} = a^{2} + 2ab + b^{2} \), where \( a = 4x \) and \( b = 3 \): \[ (4x + 3)^{2} = (4x)^{2} + 2(4x)(3) + (3)^{2} = 16x^{2} + 24x + 9. \] Now, we can substitute this back into the original expression: \[ x(4x + 3)^{2} = x(16x^{2} + 24x + 9). \] Next, we distribute \( x \): \[ x(16x^{2}) + x(24x) + x(9) = 16x^{3} + 24x^{2} + 9x. \] Therefore, the simplified answer is: \[ \boxed{16x^{3} + 24x^{2} + 9x}. \]