Evaluate $12^{3} + 13^{3} - 25^{3}$

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Solution

Let $x = 12, y = 13, z = - 25$ . Then
$x + y + z = 12 + 13 - 25 = 0$
If $x + y + z = 0,$ then $x^{3} + y^{3} + z^{3} = 3 x y z$ .
$∴ 12^{3} + 13^{3} - 25^{3} = 12^{3} + 13^{3} + (- 25)^{3} = 3 (12) (13) (- 25) = - 11700$

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