- #1

DS2C

*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 2

*ab*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?