\( 1 \leftarrow\left|\begin{array}{l}\text { Find the product. } \\ x(5 x+4)^{2}\end{array}\right| \begin{array}{l}x(5 x+4)^{2}=\square \\ \text { (Simplify your answer.) }\end{array} \)

To find the product of \( x(5x + 4)^2 \), we first need to expand \( (5x + 4)^2 \). Using the binomial expansion, we get: \[ (5x + 4)^2 = (5x)^2 + 2 \cdot 5x \cdot 4 + 4^2 = 25x^2 + 40x + 16. \] Now, multiplying this expression by \( x \): \[ x(5x + 4)^2 = x(25x^2 + 40x + 16) = 25x^3 + 40x^2 + 16x. \] Thus, the simplified form is: \[ x(5x + 4)^2 = 25x^3 + 40x^2 + 16x. \]