The material I'm reading derives Jeffrey's prior (or rather, the Fisher information for the Jeffrey's) for single-parameter binomial distribution in a manner quite similar to this Wikipedia article.
I could work out the steps until (following Wikipedia's notation, $A$ is number of successes, $B$ failures, $A+B$ total number of trials)
$$E [\frac{A}{\theta^2} + \frac{B}{(1-\theta)^2}] \\ = \frac{E[A]}{\theta^2} + \frac{E[B]}{(1-\theta)^2} $$
Maybe my background in probability calculus is just lacking, but I'm not exactly sure about the justification for this step. $E[\frac{A}{\theta^2}] + E[\frac{B}{(1-\theta)^2}]$ follows from the linearity properties of expected value, but the next step? Are we treating $\frac{1}{\theta^2}, \frac{1}{(1-\theta)^2}$ as constants?