The coefficient of xn in the expansion of (1+x)(1−x)n
(−1)nn
(−1)n(1−n)
(−1)n−1(n−1)
(n−1)
(1+x)(1−x)n=[2−(1−x)](1−x)n =2(1−x)n−(1−x)n+1
∴coefficient of xn in (1+x)(1−x)n
=2(−1)n−n+1Cn(−1)n=(−1)n(2−n−1)=(−1)n(1−n)