expel vs push out

expel

verb
  • To eject or erupt. 

  • To remove from membership. 

  • To deport. 

push out

verb
  • To extrude. 

  • To force (someone) to leave a group. 

noun
  • In nine ball pool, an optional shot after a legal break shot where a player is allowed to hit any ball first, or not any, as well as not hit a rail, and the opponent can choose who shoots the next shot. 

How often have the words expel and push out occurred in a corpus of books? (source: Google Ngram Viewer )