Use property to evaluate: $7^{3} + 3^{3} + (- 10)^{3}$

210

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- 210

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630

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- 630

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Solution

The correct option is D $- 630$
$7^{3} + (3)^{3} + (- 10)^{3}$
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,
$a = 7$
$b = 3$
$c = - 10$
and $a + b + c = 7 + 3 - 10 = 0$
Thus,
$7^{3} + 3^{3} + (- 10)^{3}$
$= 3 (7) (3) (- 10)$
$= - 630$

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