If $a = - 1, b = - 2$ and $c = - 3$ Find the value of $a b (a - b) + b c (b - c) + c a (c - a)$

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Solution

$a b (a - b) + b c (b - c) + c a (c - a)$
$= (- 1) \times (- 2) (- 1 - (- 2)) + (- 2) \times (- 3) (- 2 - (- 3)) + (- 3) \times (- 1) (- 3 - (- 1))$
$= 2 (- 1 + 2) + 6 (- 2 + 3) + 3 (- 3 + 1)$
$= 2 (1) + 6 (1) + 3 (- 2)$
$= 2 + 6 - 6 = 2$

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