Determine the product: \[ (s+11)^{2} \]

To find the product of \((s+11)^{2}\), we can use the formula for the square of a binomial, which states that \((a+b)^{2} = a^{2} + 2ab + b^{2}\). Here, \(a = s\) and \(b = 11\). Applying the formula, we get: \[ (s + 11)^{2} = s^{2} + 2(s)(11) + 11^{2} \] Calculating each term: 1. \(s^{2}\) stays as \(s^{2}\). 2. \(2(s)(11) = 22s\). 3. \(11^{2} = 121\). Now, we combine these results: \[ (s + 11)^{2} = s^{2} + 22s + 121 \] So, the final product is: \[ \boxed{s^{2} + 22s + 121} \]