Multiply and simplify. \[ (\sqrt{5}+\sqrt{11})(\sqrt{5}-\sqrt{11}) \]

To simplify \((\sqrt{5}+\sqrt{11})(\sqrt{5}-\sqrt{11})\), we can use the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \). Here, we can set: - \(a = \sqrt{5}\) - \(b = \sqrt{11}\) Using the difference of squares: \[ (\sqrt{5}+\sqrt{11})(\sqrt{5}-\sqrt{11}) = (\sqrt{5})^2 - (\sqrt{11})^2 \] Now, we compute each square: \[ (\sqrt{5})^2 = 5 \quad \text{and} \quad (\sqrt{11})^2 = 11 \] Substituting these values back into the equation, we have: \[ 5 - 11 = -6 \] Thus, the simplified result is: \[ \boxed{-6} \]