The third λ-calculus problem is a bit more advanced (although still simple):

Reduce the following expression, using the beta-rule, to no more than one term. If the expression cannot be reduced, enter "CAN'T REDUCE".

((λx.(x x)) (λx.(x x)))

"beta-reduction" is just recution by substituting variable value in the function body with its value. Check Reductions #1 and Reductions #2 for more examples.

The expression `((λx.(x x)) (λx.(x x)))`

cannot be reduced. It is easy to see that applying reduction results with exactly the same expression. So the answer is "CAN'T REDUCE".