I'm not sure what Nad is wondering about, but here's a guess.

She might be puzzled that we're calling

$$ \langle A B \rangle - \langle A \rangle \langle B \rangle $$

the covariance between $A$ and $B$. She might be more used to

$$ \langle A - \langle A \rangle \rangle \; \langle B - \langle B \rangle \rangle $$

However, these are equal! (Fun exercise.)

(**Edit: there was a typo here.**)

She might be puzzled that we're calling

$$ \langle A B \rangle - \langle A \rangle \langle B \rangle $$

the covariance between $A$ and $B$. She might be more used to

$$ \langle A - \langle A \rangle \rangle \; \langle B - \langle B \rangle \rangle $$

However, these are equal! (Fun exercise.)

(**Edit: there was a typo here.**)