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Question

Factorize the following: 8a3+b3+12a2b+6ab2


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Solution

The expression 8a3+b3+12a2b+6ab2 can be written as 2a3+b3+32a2b+32ab2 ….[1]

We know the Algebraic Identity a+b3=a3+b3+3aba+b

=a3+b3+3a2b+3ab2 …[2]

By comparing expressions [1] and [2], we can say,

8a3+b3+12a2b+6ab2 =2a3+b3+32a2b+32ab2

=2a+b3

Hence, 8a3+b3+12a2b+6ab2=(2a+b)(2a+b)(2a+b)


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