Question

Find the coefficient of xⁿ in the expansion of (1 + x) (1 – x)ⁿ .

Answer 1

To find: the coefficient of xⁿ in the expansion of (1 + x) (1 – x)ⁿ . 

Formula Used: 

Binomial expansion of (x + y)ⁿ is given by,

Thus,

Thus, the coefficient of (x)ⁿ is,

ⁿC_n-ⁿC_n-1 (If n is even)

- ⁿC_n+ ⁿC_n-1 (If n is odd)

Thus, the coefficient of (x)ⁿ is, ⁿC_n-ⁿC_n-1 (If n is even) and - ⁿC_n+ ⁿC_n-1 (If n is odd)