Final answer:
The binomial in its simplest form from the given options is '3a + 7', which already meets the criteria of a binomial with two terms. The other options either simplify to monomials or are already monomials and do not represent binomials in their simplest form.
Step-by-step explanation:
The question appears to be asking which of the provided expressions is a binomial in its simplest form. A binomial consists of two terms, which could be indicated by variables, constants, or both, and are separated by a plus or a minus sign. From the given options, the expression that is already a binomial and doesn't need further simplification is 3a + 7. This is because it consists of two terms: 3a and 7, which satisfy the criteria of a binomial.
The other expressions listed, 7a + 8a, 8ab, and 6a2, are not binomials in their simplest form. The first expression, 7a + 8a, can be simplified by combining like terms to get 15a, which is a monomial, not a binomial. The second expression, 8ab, is just one term and therefore a monomial. The third expression, 6a2, is also a single term, making it another monomial.
To eliminate terms wherever possible to simplify the algebra, you should combine like terms, as seen in the first expression 7a + 8a simplifying to 15a. Finally, always check the answer to see if it is reasonable by ensuring that all like terms have been appropriately combined and that the result conforms with the definition of a binomial.