~ましょうか (mashouka) - (N2) - Both '(よ)うか' and '~ましょうか' can be used to suggest or invite someone to do something together. '(よ)うか' is more colloquial and casual, while '~ましょうか' is more polite and formal.
~てみませんか (te mimasenka) - (N2) - '(よ)うか' and '~てみませんか' can both be used to make suggestions or invitations. '(よ)うか' is less formal and used in casual conversations, while '~てみませんか' is more polite.
~よう (you) - (N3) - '(よ)うか' and '~よう' both express intention or suggestion, but '(よ)うか' is used to invite or suggest doing something together, while '~よう' is used to express personal intention or suggestion.
Useful Vocabulary that appeared in this page
* 映画 (えいが)movie
* 観る (みる)to watch
* 食べる (たべる)to eat
* 行く (いく)to go
* 明日 (あした)tomorrow
* 遊び (あそび)play
* 飲む (のむ)to drink
* コーヒー (こーひー)coffee
Quiz
Which of the following means 'Let's go shopping tomorrow?'