come across= to find
While hiking in the mountains, we came across a small restaurant, and decided to have lunch.
bring up= to raise ( a child)
I was brought up by my sisters, because my parents died when I was young.
look after= take care of
The neighbors are looking after the cat while they´re away on holiday.
come up to= approach
Madrid is full of people coming up to you on the street to ask for donations to charity.
keep up= go at the same speed/maintain
Because my brother kept his grades up, he is allowed to play his video games on school nights.
take away= remove
If you take away his pessimism, he isn´t so bad a friend.