If two monomials are added, the sum may be a trinomial.
5xy + 9yz + 3zx + 4y
If two monomials are added, we may get a monomial or a binomial as the sum.
Consider 2a + 5a = 7a is a monomial because 2a and 5a are like terms.
2a + 5b = 2a + 5b is a binomial because 2a and 5b are unlike terms.
When a monomial is added to a monomial, we can never get trinomial.
Hence, the given statement is false.