I have to show that there exist constants $c_0,...c_n$ s.t. the polynomial $$ P(x)=y_0 \frac{(x-x_1)...(x-x_n)}{(x_0-x_1)...(x_0-x_n)} + ... + y_n \frac{(x-x_0)...(x-x_{n-1})}{(x_n-x_0)...(x_n-x_{n-1)}} $$
can be rewritten as $P(x)=c_0+c_1(x-x_0)+c_2(x-x_0)(x-x_1)+...+c_n(x-x_{n-1})$
How can I show that such constants exist, and ultimately find them?
Thanks in advance!