"Bring the menu, please."
Translation:Принесіть меню, будь ласка.
A plural polite form use to conversation with older person, boss and an unfamiliar adult person or even younger person, if you want to be very polite with whom or kidding :)
A singular polite form use in all other situation when you want to be polite (with your wife, children, staff etc).
A plural/singular imperative form use when you don't have time or when not necessary to be polite.
There is an playful Ukrainian folk song "Да й куди їдеш, Явтуше?" https://www.youtube.com/watch?v=8olJ1cGmH18
A girl asks different questions to a boy and the boy always answers "Не скажу" - "I will not say", but then, when she says "Та коли ж твоя добра ласка, то й скажеш" - "If you will be very kind to me then you will say", the boy answer to her question. "Будь ласка" have a similar meaning and action :)
P. S. There is even cartoon https://www.youtube.com/watch?v=nQYmyMCw2iY and many other https://www.youtube.com/results?search_query=%D0%94%D0%B0+%D0%B9+%D0%BA%D1%83%D0%B4%D0%B8+%D1%97%D0%B4%D0%B5%D1%88%2C+%D0%AF%D0%B2%D1%82%D1%83%D1%88%D0%B5