The paper improves the generalized F - expansion method, expands the power frequency of function F from - N to N , and proposes some new F function of different equations. The paper subsequently applies this method to the KdV equation with variable coefficients so that many new exact solutions for these equations are obtained%对F-展开法作了适当的扩充：让F函数的幂扩充为从-N次到N次的形式，同时让F满足不同形式的方程，得到不同形式的，函数，从而得到更多形式的精确解，并利用扩充了的F展开法给出了变系数KdV方程的更多形式的精确解．
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