Expansion is an important method for the testing of the validity or invalidity of PredL sequents. It can always be used, but sometimes gets messy. There is one proviso, however. Also, if there are any proper names given in the sequent itself, they must be included in the UD we use for the expansion. That would not make sense.
Expansion is a skill which takes practice.
What you should be able to see from these examples, esp. The Method of Expansions will always work in order to determine the validity or invalidity of a PredL sequent, but it can be cumbersome and inefficient. If we derive until we obtain minimals, then we use a t-table test on the minimals and see whether it is possible for all of the minimals to be true at the same time. If all of the minimals can be true at the same time, the original sequent is INvalid. If it is not possible for all of the minimals to be true at the same time, then we will find a contradiction among the values of the minimals and, again, that will be proof of validity.