have a ulterior motives と have an agenda と you are up to something と have an axe to grind はどう違いますか？説明が難しい場合は、例文を教えて下さい。

"have an ulterior motive" means the person you're speaking about is trying to hide what they're really trying to do. For example, "He said he wanted to hang out at my house, but I think he has an ulterior motive, because he's always liked my sister!"

"have an agenda" can mean the same as an ulterior motive, but an agenda can also just be an ordered plan. You can send meeting participants an agenda for the meeting so they know what will be talked about. If you have a secret agenda, it's like having an ulterior motive.

"have an axe to grind" also means the same as "ulterior motive", but it is most commonly used to mean to have a grudge or dispute to take up with someone.

"you are up to something" means the speaker suspects the person they're talking about has an ulterior motive, but this phrase can be used for positive things while the others are almost always negative. "My husband and son have been whispering a lot and they stop talking when I walk in the room. My birthday's next week and I think they are up to something!"