expense vs write down

expense is a noun but write down is not a noun.

Word	Noun	Adjective	Verb	Adverb
expense	Yes	No	Yes	No
write down	No	No	Yes	No

As verbs, expense and write down are synonyms defined as:

Other synonyms of expense include write off.

expense (noun)	write down (noun)
a detriment or sacrifice
amounts paid for goods and services that may be currently tax deductible (as opposed to capital expenditures)
money spent to perform work and usually reimbursed by an employer

expense (verb)	write down (verb)
reduce the estimated value of something	reduce the estimated value of something
	put down in writing; of texts, musical compositions, etc.