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Question
a3 + 8b3 + 64c3 - 24abc
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Solution
a3 + 8b3 + 64c3 - 24abc
= (a)3 + (2b)3 + (4c)3 - 3 × a × 2b × 4c
= (a + 2b + 4c)(a2 + (2b)2 + (4c)2 - a × 2b - 2b × 4c - 4c × a) [∵ a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)]
= (a + 2b + 4c)(a2 + 4b2 +16c2 - 2ab - 8bc - 4ac)
∴ a3 + 8b3 + 64c3 - 24abc = (a + 2b + 4c)(a2 + 4b2 +16c2 - 2ab - 8bc - 4ac)
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