Solve the given expression
$a^{2} (b - c) + b^{2} (c - a) + c^{2} (a - b)$

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Solution

$a^{2} (b - c) + b^{2} (c - a) + c^{2} (a - b)$
$\Rightarrow a^{2} b - a^{2} c + b^{2} c - b^{2} a + c^{2} (a - b)$
$\Rightarrow (a^{2} b - b^{2} a) + (b^{2} c - c^{2} b) + (c^{2} a - a^{2} c)$
$\Rightarrow a b (a - b) + b c (b - c) + c a (c - a)$
$= a b (a - b) + b c (b - c) + c a (c - a)$

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