The value of $45^{3} - 65^{3} - 20^{3}$ is __________.

175500

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- 191500

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170000

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- 170000

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Solution

The correct option is C $- 191500$
$a^{3} - b^{3} - c^{3} = (a - b - c)^{3} + 3 a b (a - b) + 3 b c (b + c) + 3 a c (a - c) - 6 a b c$
putting $a = 45, b = 65, c = 20$
$45^{3} - 65^{3} - 20^{3} = (- 40)^{3} + 3 \times 2925 (- 20) + 3 \times 1300 (85) + 3 \times 900 (25) - 6 \times 58500$
$= - 191500$

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