Let a and b be positive real numbers. Prove that (a+2)(b+2)(a+b) > 16ab
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By AM–GM, $\displaystyle a+2\ \ge\ 2\sqrt{2a}$ $\displaystyle b+2\ \ge\ 2\sqrt{2b}$ $\displaystyle a+b\ \ge\ 2\sqrt{ab}$ The result follows.
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