  Waring problem for forms is important and classical in mathematics. It has
been widely investigated because of its wide applications in several areas. In
this paper, we consider the Waring problem for binary forms with complex
coefficients. Firstly, we give an explicit formula for the Waring rank of any
binary binomial and several examples to illustrating it. Secondly, we prove
that, up to scalar multiplication, there are exactly $\binom{d-1}{2}$ binary
forms of degree $d$ with Waring rank two and multiple of three fixed distinct
linear forms.
