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.
((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".