perfect vs brush up

perfect is a noun but brush up is not a noun.

Word	Noun	Adjective	Verb	Adverb
perfect	Yes	Yes	Yes	No
brush up	No	No	Yes	No

As verbs, brush up is a hyponym of perfect; that is, brush up is a word with a more specific, narrower meaning than perfect:

Other hyponyms of perfect include optimise, optimize, polish, polish up, round, round off.

perfect (noun)	brush up (noun)
a tense of verbs used in describing action that has been completed (sometimes regarded as perfective aspect)

perfect (adjective)	brush up (adjective)
being complete of its kind and without defect or blemish
precisely accurate or exact
without qualification; used informally as (often pejorative) intensifiers

perfect (verb)	brush up (verb)
make perfect or complete	bring to a highly developed, finished, or refined state
	refresh one's memory