Which of the following expressions is not a binomial?

Let us check each option one by one.

Option A: 7mn + m

Since the given expression contains two terms, it is a binomial.

Option B: a² + b²

Since the given expression contains two terms, it is a binomial.

Option C: z² − 3z + 8

Since the given expression contains three terms, it is a trinomial.

Option D: z² + z

Since the given expression contains two terms, it is a binomial.

Hence, the expression z² − 3z + 8 is the correct alternative.