mathematical product vs product

mathematical product and product both are nouns.

Word	Noun	Adjective	Verb	Adverb
mathematical product	Yes	No	No	No
product	Yes	No	No	No

As nouns, mathematical product and product are synonyms defined as:

mathematical product (noun)	product (noun)
a quantity obtained by multiplication	an artifact that has been created by someone or some process
	items for sale to the individual consumer
	a quantity obtained by multiplication
	the set of elements common to two or more sets
	a consequence of someone's efforts or of a particular set of circumstances
	a chemical substance formed as a result of a chemical reaction