You say 'Goodbye' to someone when you or they are leaving, or at the end of a telephone conversation.
goodbyes
When you say your goodbyes, you say something such as 'Goodbye' when you leave.
He said his goodbyes knowing that a long time would pass before he would see his child again.
他道了别,清楚要过很久才能再见到他的孩子。
Perry and I exchanged goodbyes.
我和佩里互相道了别。
say goodbye to something , wave goodbye to something
If you say goodbye or wave goodbye to something that you want or usually have, you accept that you are not going to have it.
He has probably said goodbye to his last chance of Olympic gold.
他或许已经失去了夺取奥运金牌的最后机会。