Find the product. \[ \begin{array}{l}2(x+6)^{2}\end{array} \] \( 2(x+6)^{2}=\square \) (Simplify your answer. Use integers or fractions for any numbers in the exp

To find the product of \( 2(x+6)^{2} \), we first expand \( (x+6)^{2} \): \[ (x+6)^{2} = x^{2} + 12x + 36 \] Now, multiply this result by \( 2 \): \[ 2(x+6)^{2} = 2(x^{2} + 12x + 36) = 2x^{2} + 24x + 72 \] Thus, simplifying gives us: \[ 2(x+6)^{2} = 2x^{2} + 24x + 72 \]