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State True or False. There exist a pair of non negative real numbers $$a$$, $$b$$ such that $$(a - b)\left(a(a + b) - 2b^2\right)$$ is negative.
Correct Answer: False
$$a(a + b) - 2b^2 = a^2 + ab - 2b^2 = (a - b)(a + 2b)$$. So the expression is $$(a - b)^2(a + 2b)$$, which is never negative for $$a, b \ge 0$$. The statement is False.
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