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Factorize:a3 + 8b3 + 64c3 − 24abc |
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Answer» a3 + 8b3 + 64c3 − 24abc = (a)3 + (2b)3 + (4c)3− 3 x a x 2b x 4c [Using a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca)] = (a + 2b + 4c)(a2 + (2b)2 + (4c)2 −a x 2b − 2b x 4c − 4c x a) = (a+2b+4c)(a2 +4b2 +16c2 −2ab−8bc−4ac) Therefore, a3 + 8b3 + 64c3 − 24abc = (a+2b+4c)(a2 +4b2 +16c2 −2ab−8bc−4ac) |
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