Please use markdown formatting:

(x - 2y) * (x + 2y) = x * x + x * 2y - 2y * x - 2y * 2y = x * x + (x * 2y - 2y * x) - 2y * 2y = x * x - 4y * y

or KaTeX:

$ (x - 2y) * (x + 2y) = x * x + x * 2y - 2y * x - 2y * 2y = x^2 + (x * 2y - 2y * x) - 4y^2 = x^2 - 4y^2 $

to write mathematical formulas.

(x - 2y) * (x + 2y) = xx + x2y - 2yx - 2y2y = xx + (x2y - 2yx) - 2y2y = xx - 4yy

because a^2 - b^2 = (a+b)(a-b).
This is an algebraic identity - the difference of two squares
In your case, you can treat x =a, and b = 2y.

https://mste.illinois.edu/dildine/times/diff2sq.pdf

could somebody please explain to me why x2 - 4 * y2 = (x - 2y) * (x + 2y)?

It would be redundant: https://en.wikipedia.org/wiki/Product_(mathematics)

At least you should mention elements multiplication somewhere "The Product of all the elements multiplied" something like that..

RegEX harder than chinese for me.

oh man you're making life difficult for us, whenever I see a RegEX I let go.

Please use a spoiler flag.

jo thank you man, now I see it, but yesterday I got a wired error message, which said unauthorized.