product vs mathematical product

product and mathematical product both are nouns.

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

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

product (noun)	mathematical product (noun)
an artifact that has been created by someone or some process	a quantity obtained by multiplication
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