Problem: Evaluate the product $ (\sqrt{5}+\sqrt{6}+\sqrt{7})(\sqrt{5}+\sqrt{6}-\sqrt{7})(\sqrt{5}-\sqrt{6}+\sqrt{7})(-\sqrt{5}+\sqrt{6}+\sqrt{7}) $ Solution: We may group terms however we'd like, so we simplify as follows: $ \begin{align*} EXP & = -\left((\sqrt{5} +\sqrt{6} )^2-7\right) \left((\sqrt{5} -\sqrt{6} )^2 - 7\right) \\ & = -\left(\left(\left(\sqrt{5} +\sqrt{6} \right) \left(\sqrt{5} - \sqrt{6} \right)\right )^2 - 7 \left(\left(\sqrt{5} + \sqrt{6} \right)^2 + \left(\sqrt{5} -\sqrt{6} \right)^2 \right) +49 \right) \\ & = 50 - 7\left((5+6) + (5+6)\right) \\ & = 106 \end{align*} $