In Dodelson's Book, chapter 3, we have the collision term in Boltzmann equation is written as
$$\int\frac{d^3p_1}{(2\pi)^32E_1}\int\frac{d^3p_2}{(2\pi)^32E_2}\int\frac{d^3p_3}{(2\pi)^32E_3}\int\frac{d^3p_4}{(2\pi)^32E_4}(2\pi)^4\delta^3(p_1+p_2-p_3-p_4)\delta(E_1+E_2-E_3-E_4)\{f_1f_2[1\pm f_3][1\pm f_4]-f_3f_4[1\pm f_1][1\pm f_2]\}$$
I want to understand why the distribution functions are related as $$f_1f_2(1\pm f_3)(1\pm f_4)-f_3f_4(1\pm f_1)(1\pm f_2)$$ and not as in the classical form $ f_1f_2 - f_3f_4$.
Thanks.