I've been told, a binomial is an expression having only 2 terms.
So, is $(x+y)^2 $ also a binomial? Shouldn't it be a trinomial as it would expand into $x^2 + 2xy + y^2 $? Then, if $(x+y)^2 $ is a trinomial. Why did they name it's expansion method, "Binomial Theorem"? Why not call it "Polynomial Theorem"?
A binomial is the sum of two monomials $a$ and $b,$ i.e. $a+b$. The binomial theorem describes the algebraic expansion of powers of a binomial, i.e. $(a+b)^k.$ A generalization of this is the multinomial theorem that describes the expansion of the sum of $m$ monomials, i.e. $(a_1+a_2+...+a_m)^k.$ So, the name refers to the number of summands that are taken some power $k$.