What kind of formula is this and how is it to be retraced?

[SansaStark]

This is basic maths but I kind of forgot how to retrace such an equation.
My question is: why does "+-2*xi(n-1)*delta" which is in the middle of the first long equation cancle out? I'm thankful for an answer!

 

[Fightfish]

The context is missing, but I'll guess that this is random walk?
For a random walk process, what do you think is the average displacement?
Another way to look at it would be to consider the \pm signs - how many particles do you think will move in the + direction and how many in the - direction?

 

[SansaStark]

Yeah, it is the random walk! :)
Do you mean that the middle part equals zero (all negatives and positive deltas are on average 0) and that's why it can be canceled out?
I thought it was some formula like (a+b)(a-b) where it's a²-ab+ab-b² where the inner parts just cancels out each other.