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since abc ≠ 0 , we know that either all numbers can be +ve or any two can be -ve

Option A does not help to solve the problem since we can not make out that which numbers can be -ve and value changes with every trial and error method. Therefore, A can not be the answer.

Option B tells us that A+B+C=0, therefore we can use the formula that

\(a^3 + b^3 + C^3 - 3abc = (a+b+c) (a^2 + b^2 + c^2 - ab - bc - ac)\)

and since we know that a+b+c = 0 then \(a^3 + b^3 + c^3 = 3abc\)

And thus putting "3abc" at the place of \(a^3 + b^3 + c^3\), will give us the answer. Therefore answer is "B"

Only thing that since I know the formula thats why I could solve this problem within seconds ..... how to solve if we do not know the formula .... please someone explain.

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