\( 1 \& \quad \) Find the product. \( x(2 x+1)^{2} \) \( \begin{array}{l}x(2 x+1)^{2}=\square \\ (\text { Simplify your answer.) }\end{array} \)

To find the product \( x(2x+1)^{2} \), let's first expand \( (2x+1)^{2} \). Using the formula \( (a+b)^{2} = a^{2} + 2ab + b^{2} \), where \( a = 2x \) and \( b = 1 \): \[ (2x+1)^{2} = (2x)^{2} + 2(2x)(1) + 1^{2} = 4x^{2} + 4x + 1. \] Now, substitute this back into the expression: \[ x(2x+1)^{2} = x(4x^{2} + 4x + 1). \] Next, distribute \( x \) into each term: \[ = 4x^{3} + 4x^{2} + x. \] So, the simplified expression is: \[ x(2x+1)^{2} = 4x^{3} + 4x^{2} + x. \] Thus, the final answer is \( \boxed{4x^{3} + 4x^{2} + x} \).