Find the product. \[ \begin{array}{l}3(x+5)^{2}\end{array} \] \( \begin{array}{l}3(x+5)^{2}=\square \\ \text { (Simplify your answer. Use integers or fractions for any numbers in the expression.) }\end{array} \)

To find the product \( 3(x+5)^{2} \), we first need to expand \( (x+5)^{2} \). Using the formula \( (a+b)^{2} = a^{2} + 2ab + b^{2} \), where \( a = x \) and \( b = 5 \): \[ (x+5)^{2} = x^{2} + 2 \cdot x \cdot 5 + 5^{2} = x^{2} + 10x + 25 \] Now, we multiply this result by 3: \[ 3(x+5)^{2} = 3(x^{2} + 10x + 25) \] Distributing the 3, we get: \[ 3(x^{2}) + 3(10x) + 3(25) = 3x^{2} + 30x + 75 \] Thus, the simplified answer is: \[ 3(x+5)^{2} = 3x^{2} + 30x + 75 \]