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Question
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Solution
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
= 3a(9a2 + 4b2 + c2 - 6ab + 2bc + 3a) + 2b (9a2 + 4b2 + c2 - 6ab + 2bc + 3ca) - c(9a2 + 4b2 + c2 - 6ab + 2bc + 3ca)
= 27a3 + 12ab2 + 3ac2 - 18a2b + 6abc + 9a2c + 18a2b + 8b3 + 2bc2 - 12ab2 + 4b2c + 6abc - 9a2c - 4b2c - c3 + 6abc - 2bc2 - 3ac2
= 27a3 + 8b3 - c3 + 18abc.
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