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Cube Numbers

If a-b=6, the...

Question

If $a - b = 6$ , then find the value of $a^{3} - b^{3} - 18 a b$

A

108

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B

216

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C

36

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D

54

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Solution

The correct option is B
216

Given: $a - b = 6$

Taking cube of the given equation, we get

$(a - b)^{3} = 6^{3} = 216$

$\Rightarrow a^{3} - b^{3} - 3 a b (a - b) = 216$

$\Rightarrow a^{3} - b^{3} - 3 a b \times 6 = 216$

$\Rightarrow a^{3} - b^{3} - 18 a b = 216$

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