\( 1 \leftarrow \begin{array}{l}\text { Find the product. } \\ x(4 \mathrm{x}+3)^{2}\end{array} \left\lvert\, \begin{array}{l}x(4 \mathrm{x}+3)^{2}=\square \\ \text { (Simplify your answer.) }\end{array}\right. \)

To find the product \( x(4x + 3)^2 \), we first need to expand \( (4x + 3)^2 \). This can be done using the formula \( (a + b)^2 = a^2 + 2ab + b^2 \): 1. Here, \( a = 4x \) and \( b = 3 \). 2. Calculating \( a^2 \): \( (4x)^2 = 16x^2 \). 3. Calculating \( 2ab \): \( 2 \cdot 4x \cdot 3 = 24x \). 4. Calculating \( b^2 \): \( 3^2 = 9 \). So, we have: \[ (4x + 3)^2 = 16x^2 + 24x + 9. \] Now, we multiply this result by \( x \): \[ x(4x + 3)^2 = x(16x^2 + 24x + 9) = 16x^3 + 24x^2 + 9x. \] Therefore, the simplified answer is: \[ x(4x + 3)^2 = 16x^3 + 24x^2 + 9x. \]