Is the sum of two monomials always a monomial? Is their product always a monomial?

Sum of two monomials is not necessarily always a monomial.For example:Suppose we have two monomials as 2x and 5x. Adding 2x+5x , we get 7x.So if two monomials are both like terms then their sum will be a monomial.Suppose we have two monomials as 3y and 4xNow these are both monomials but unlike, so we cannot add them together and sum would be 3y + 4x , which is a binomial.So if we have like terms then the sum is monomial but if we have unlike terms sum is binomial.Product of monomials:suppose we have 2x and 5y, Product : 2x*5y = 10xy ( which is a monomial)So yes product of two monomials is always a monomial.