Use 'brush up' to describe a quick review, not deep learning or studying something completely new. I'll brush up on the state capitals before the quiz tomorrow.
Pro Tip 2/3
Informal Tone
'Brush up' is casual and usually used in everyday conversation or less formal writing. Let's brush up on those dance moves before the party.
Pro Tip 3/3
Skill Oriented
Often refers to practical skills or knowledge, like languages or musical instruments. I need to brush up on my piano skills before the recital.