Lambda Calculus Equivalence I'm a bit new to lambda calculus and was wondering about the equivalence of two expressions 
$$(\lambda x.\lambda y.xy)\lambda z.z\overset{?}=(\lambda x.\lambda y.xy)(\lambda z.z)$$
Can anyone help out?

By convention the outer most parenthesis are dropped for minimal clutter.
$$\color{red}{(\lambda x.\lambda y.xy)}\color{blue}{\lambda z.z}\iff\color{red}{(\lambda x.\lambda y.xy)}\color{blue}{(\lambda z.z)}$$
The same thing is done in algebra:
$$\color{red}{(z)}\color{blue}{(x+y)}\iff \color{red}z\color{blue}{(x+y)}$$
In lambda calculus there is a similar "order of operations" as in conventional mathematics. Things to note are parenthesis are evaluated first.
