Use property to evaluate: $13^{3} + (- 8)^{3} + (- 5)^{3}$

1560

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1770

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2197

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1331

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Solution

The correct option is D $1560$
$13^{3} + (- 8)^{3} + (- 5)^{3}$
We know that
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - a c - b c)$
If $(a + b + c) = 0$ , then.
$a^{3} + b^{3} + c^{3} = 3 a b c$
Here,
$a = 13$
$b = - 8$
$c = - 5$
and $a + b + c = 13 - 8 - 5 = 0$
Thus,
$13^{3} + (- 8)^{3} + (- 5)^{3}$
$= 3 (13) (- 8) (- 5)$
$= 1560$

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