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The coefficient of x¹⁸ in the product (1 + x)(1 − x)¹⁰(1 + x + x²)⁹ is:

1. 126
2. −84
3. −126
4. 84

Correct answer: 84

Solution

To find the coefficient of x¹⁸ in the product, we can expand each factor and combine terms. The positive contributions from the factors (1 + x) and (1 + x + x²)⁹, along with the negative contributions from (1 − x)¹⁰, lead to a net coefficient of 84 for x¹⁸.

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