How many different expressions can you get by inserting parentheses into: $x_{1}-x_{2}-\cdots-x_{n}$? I ran into this question and I am finding it very difficult to solve:

How many different expressions can you get by inserting parentheses into:
  $$x_{1}-x_{2}-\cdots-x_{n}\quad ?$$

For example:
$$\begin{align*}
x_{1}-(x_{2}-x_{3}) &= x_{1}-x_{2}+x_{3}\\
(x_{1}-x_{2})-x_{3}&=x_{1}-x_{2}-x_{3}\\
x_{1}-(x_{2}-x_{3})-x_{4})&=x_{1}-x_{2}+x_{3}+x_{4}\\
\end{align*}$$
I'm really desperate for a full answer. I've been working on this for 3 hours. Thanks in advance.

HINT: No matter how you parenthesize the expression, when you clear the parentheses, the first two terms will be $x_1-x_2$. Show by induction that the remaining $n-2$ signs can be any combination of plus and minus signs, meaning that for $n\ge 2$ you get $2^{n-2}$ distinct expressions.
