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Question

Which of the following is an expansion of the identity (ab)3?


A

a3+b33a2b+3ab2

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B

a3b3+3a2b3ab2

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C

a3b33a2b+3ab2

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D

a3b33a2b3ab2

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Solution

The correct option is C

a3b33a2b+3ab2


(ab)3=(ab)(ab)2
=(ab)(a22ab+b2)
=a32a2b+ab2a2b+2ab2b3
=a3b33a2b+3ab2


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