Parseval's Theorem - Average Power of the difference of functions

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Homework Statement:

Given a function [itex] e(t) = f(t) - g(t) [/itex], find the average power of the function.

Relevant Equations:

Parseval's theorem
Hi,

So I have a quick conceptual question about Parseval's theorem in this application. In previous parts of this question, we have found the average powers of both [itex] f(t) [/itex] and [itex] g(t) [/itex] by integration and using the complex Fourier series respectively (not sure if this is relevant to my question). I wanted to know how do we use these to calculate the average power of e(t)?

The answer simply does subtract the two aforementioned expressions to get the answer. However, I was wondering why we wouldn't need to consider the 'cross-terms'? So in the average power integral, we are dealing with [itex] |e(t)|^2 = |e(t)||e^*(t)| = |f(t) - g(t)||g^*(t) - f^*(t)| [/itex] and wouldn't this contain terms that look like [itex] f(t) g^*(t) [/itex] and [itex] f^*(t) g(t) [/itex] (omitting the signs for now)? The calculation that they have done does not include any of these and I was wondering whether we are allowed to combine average powers like that?

Thanks in advance.

(N.B. I do understand that this might be question-specific, but just want to understand the concept first as this is the last sub-part of a longer question and typing that out would include seemingly redundant information - I can include it if necessary)
 

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