Let $a , b \in \mathbb R$. Then $$ | a^3 + a^2 b + ab^2 + b^3 | \leqslant |a + b|^3 $$ holds?
$ | a^3 + ab^2 + a^2 b + b^3 | \leqslant |a + b|^3 $ holds??
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inequality
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1If you require $a,b\geq 0$ then yes. Otherwise, no. – 2012-07-01