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Question

a3 - b3 is always divisible by:


A

a - b

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B

a × b

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C

a + b

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D

2a + b

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Solution

The correct option is A

a - b


Take a=2 and b=1 and check.
Alternatively, we know the algebraic identity,

a3b3=(ab)(a2+2ab+b2)

Hence , we can see that (ab) is a factor of a3 - b3
Thus, a3 - b3 is divisible by (ab)


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