Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$ 
Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$

I know that 
\begin{equation*}
(1 + x)^n = 1 + nx +\frac {n(n-1)}2!\cdot x^2 +\frac {n(n-1)(n-2)}3! \cdot x^3 +...    
\end{equation*}
but how can I use it to solve the above problem>Is there any other easier way to do it ?

$$
(x+1)^n=((x-1)+2)^n=2^n+n 2^{n-1}(x-1)+\binom{n}{2}2^{n-2}(x-1)^2+(x-1)^3 \cdot F(x)
$$
So the remainder is $$2^n+n 2^{n-1}(x-1)+\binom{n}{2}2^{n-2}(x-1)^2.$$
