The formula that you have provided is simply a rearrangement of the standard formula for the calculation of covariance.

The standard measure of the covariation of two variables is E[(Xi - X)(Yi - Y)] .

Expanding this expression obtains
E[XiYi - XYi - XiY + XY]
In the case where E(Xi) = E(Yi) = 0 the expanded form reduces to
E[XiYi + XY]. This is very close to the expression described by your author.

In the above expression E is the expected value operator, Xi and Yi are the values of the variables X and Y for the ith observation, and X and Y are the mean values for the variables X and Y. Please forgive the double meaning of the symbols X and Y in the above explanation. It is difficult to write X-bar and Y-bar in ASCII script.

You could also use the terms

reduced expression
reordered expression
rearranged expression

Depending on the overall context of your text good substitutes for the word "expression" might also include "term", "equation", and "formula".

As more than just factoring takes place in the above reduction, I would shy away from the term "factor".

Covariance is very basic to statistical analysis, and can be found in any book on elementary statistics.

Source: my own brain and many hours of training in statistics and econometrics.

Credits: several very patient, perhaps even brilliant instructors and authors of excellent textbooks.