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In the expansion of (1 + x)(1 - x)ⁿ, what is the coefficient of xⁿ?

1. (-1)^(n-1) n
2. (-1)ⁿ (1 - n)
3. (-1)^(n-1) (n - 1)²
4. (n - 1)

Correct answer: (-1)ⁿ (1 - n)

Solution

The correct option is derived from the binomial expansion of (1 - x)ⁿ, where the coefficient of xⁿ is influenced by the multiplication with (1 + x). This results in the coefficient being (-1)ⁿ multiplied by (1 - n), reflecting the alternating sign and the linear relationship with n.

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