# The coefficient of $x^n$ in the expansion $(1+x)(1-x)^n$ is

$\begin{array}{1 1} =(-1)^n [1-n] \\ =(-1)^n [1+n] \\ =(-1)^{n-1} n \\ =(-1)^n [n-1] \end{array}$

Coefficient of $x^n$ in $(1+x)(1-x)^n$$= 1\times coeff. of x^n in (1-x)^n+1\times coeff. of x^{n-1} in (1-x)^n \therefore Coefficient of x^n in (1+x)(1-x)^n$$=(-1)^n $$^nC_n$$+(-1)^{n-1}$$^nC_{n-1}$
$=(-1)^n [1-n]$