Question
Simplify:$(3a + 2b - c)(9a^2 + 4b^2 + c^2 - 6ab + 2bc +3ca)$
✓
Answer
$(3a + 2b - c)(9a^2 + 4b^2 + c^2 - 6ab + 2bc +3ca)$
$= 3a(9a^2 + 4b^2 + c^2 - 6ab + 2bc + 3a) + 2b (9a^2+ 4b^2 + c^2 - 6ab + 2bc + 3ca) - $$c(9a^2 + 4b^2 + c^2 - 6ab + 2bc + 3ca)$
$= 27a^3 + 12ab^2 + 3ac^2 - 18a^2b + 6abc + 9a^2c + 18a^2b + 8b^3 + 2bc^2 - 12ab^2 + $$4b^2c + 6abc - 9a^2c - 4b^2c - c^3 + 6abc - 2bc^2 - 3ac^2$
$= 27a^3 + 8b^3 - c^3 + 18abc.$
$= 3a(9a^2 + 4b^2 + c^2 - 6ab + 2bc + 3a) + 2b (9a^2+ 4b^2 + c^2 - 6ab + 2bc + 3ca) - $$c(9a^2 + 4b^2 + c^2 - 6ab + 2bc + 3ca)$
$= 27a^3 + 12ab^2 + 3ac^2 - 18a^2b + 6abc + 9a^2c + 18a^2b + 8b^3 + 2bc^2 - 12ab^2 + $$4b^2c + 6abc - 9a^2c - 4b^2c - c^3 + 6abc - 2bc^2 - 3ac^2$
$= 27a^3 + 8b^3 - c^3 + 18abc.$
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