Questions & Answers about Мы разделили пирог поровну и начали пить чай.
Yes, it can.
Russian often leaves out subject pronouns when the subject is clear from context. So Разделили пирог поровну и начали пить чай can be a perfectly natural sentence.
One small detail: in the past tense, Russian verbs show number and, in the singular, gender, but they do not show person clearly the way present-tense verbs do. So разделили and начали tell you that more than one person did the action, but not automatically that it was we. Because of that, мы is useful when the speaker wants to make the subject explicit.
Разделили is:
- past tense
- plural
- perfective
- from разделить
The perfective aspect is used because the dividing is presented as a completed action. The idea is:
- first, we finished dividing the pie,
- then, we began drinking tea.
If you used an imperfective verb such as делили or разделяли, the focus would be more on the process of dividing, not on its completion.