write up, write down

write up

1. to write a report, article etc using notes that you wrote earlier

- Now the experiments are completed, he just has to write up his findings.

2. to report officially that someone has done something wrong

write down

to write something on a piece of paper

- Write down seven words that describe how you feel.

- As soon as I have an idea, I write it down.

출처 : Macmillan Dictionary