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 ?

By setting $y=x-1$, we just have to find the remainder of $(y+2)^n$ when divided by $y^3$.
By the binomial theorem:
$$(y+2)^n \equiv 2^n + n2^{n-1} y + n(n-1)2^{n-3} y^2\pmod{y^3}.$$
