$$ A = \begin{vmatrix} 0 & 1 & 1 & 1 & \dots & 1 \\ 1 & a_1 & x & x &\dots & x \\ 1 & y & a_2 & x & \dots & x \\ 1 & y & y & a_3 & \dots & x\\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 1 & y & y & y &\dots& a_n \end{vmatrix}$$
as we define: $\ f(x) = (a_1-x)(a_2-x) \cdots (a_n-x), \ f(y) = (a_1 -y)(a_2 -y) \cdots (a_n -y) $
Prove that: $det(A) = \frac{f(x)-f(y)}{x-y}$
It isn't very clear how to get an answer. Help me please.