Concept:
Bauxite is an important ore of aluminium. It is mainly a hydrated oxide of aluminium.
Step 1: Aluminium oxide is:
\[
Al_2O_3
\]
Step 2: Bauxite is not pure anhydrous aluminium oxide. It contains water of hydration.
Step 3: The commonly represented formula of bauxite is:
\[
Al_2O_3\cdot 2H_2O
\]
Step 4: Since bauxite is a hydrated aluminium oxide, the correct formula among the given options is:
\[
\boxed{Al_2O_3\cdot 2H_2O}
\]