Show that two summations are equivalent 
Show that
  $$
\sum_{i=1}^n \left(x_i - \bar{x}\right) \left(y_i - \bar{y}\right)
= \left(\sum_{i=1}^n x_i y_i\right) - n \bar{x} \bar{y}.
$$

My work is attached:
.
I'm stuck on what I should do next. 
Any guidance in the right direction would be great!

Hint: 
Use $\sum_{i=1}^{n} \bar{x} y_i = \bar{x} \sum_{i=1}^{n}  y_i = n \bar{x} \bar{y}$ and $\sum_{i=1}^{n} \bar{y} x_i = n \bar{x} \bar{y}$.
