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The coefficient of $x^{18}$ in the product $(1+x)(1-x)^{10}(1+x+x^2)^9$ is:
(1) 84 (2) $-126$ (3) $-84$ (4) 126
Simplifies to $(1-x^3)^9(1-x)$. Coefficient of $x^{18}$: ${}^9C_6 = 84$.
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