Use property to evaluate: $9^{3} - 5^{3} - 4^{3}$ .

540

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365

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280

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167

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Solution

The correct option is B $540$
$9^{3} + (- 5)^{3} + (- 4)^{3}$
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,
$a = 9$
$b = - 5$
$c = - 4$
and $a + b + c = 9 - 5 - 4 = 0$
Thus,
$9^{3} + (- 5)^{3} + (- 4)^{3}$
$= 3 (9) (- 5) (- 4)$
$= 540$

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