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Question -

Factorize each of the following expressions:
a3 + 8b3 + 64c3 тАУ 24abc



Answer -

We know that
a3 + b3 + c3 тАУ 3abc = (a + b +c) (a2 + b2 + c2 тАУ ab тАУ bc тАУ ca)
a3 + 8b3 + 64c3 тАУ 24abc
= (a)3 + (2b)3 + (4c)3 тАУ 3 x ax 2b x 4c
= (a + 2b + 4c) [(a)2 + (2b)2 + (4c)2 -ax 2b тАУ 2b x 4c тАУ 4c x a]
= (a + 2b + 4c) (a2 + 4b2 + 16c2 тАУ2ab тАУ 8bc тАУ 4ca)

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