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Question
Simplify: (2a + 3b + 4c) (4a2 + 9b2 + 16c2 – 6ab – 12bc – 8ca)
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Solution
(2a + 36 + 4c) (4a2 + 9b2 + 16c2 – 6ab – 12bc – 12bc – 8ca)
We know that
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 × 3 abc
∴ (2a + 36 + 4c)(4a2 + 9b2 + 16 c2 – 6 ab – 12 bc – 8 ca)
= (2a)3 + (3b)3 + (4c)3 – 3 × 2a × 36 × 4c
= 8a3 + 27b3 + 64c3 – 72 abc
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