I'm starting with my self studying of math with Algebra I. The text I'm using is Gelfand and Shen's Algebra. I'm at the point where it talks about the Formula for the Square of the Sum, The Square of the Distance Formula, and The Difference of Squares Formula. In going over this, I understand that the formula for the square of the sum is essentially saying the following: If a boys each received a candies, they would walk away with a total of ##a^2## candies. If b girls each received b candies, they would walk away with a total of ##b^2## candies. In using this same scenario, but the boys received ab candies and the girls received ba candies, they would walk away with 2ab more than the previous scenarios. This equation is listed below. $$\left(a+b\right)^2~=~a^2+b^2+2ab$$ Now I understand this logic, however in looking at the other two formulas, ##\left(a-b\right)^2~=~a^2-2ab+b^2## (the square of the distance formula) as well as ##a^2-b^2~=~\left(a+b\right)\left(a-b\right)## (the difference of squares formula), I cant put together a scenario in which these could be used in a scenario like in the first example. Could someone give me some insight into what these last two are exactly use for?