Tuesday, February 25, 2014

Binomial Expansion

Today we will learn how to expand a binomial into its fully expanded form. There are 2 ways. 
One way is the binomial therom
(A+b)^n
All you do is foil the entire thing to the nth time. Yah its a ton of work no fun. 
The other way is to use pasacals triangle. Much more fun cause it is a ton easier. 
A lot easier. How? Well you see that row 0,1,2... And so on well that corresponds to the n power of your equation. 
How do you do this. You take the coeffiecents that are needed then you multiply by the correct term. How do you eo this? Well it is quite simple. First take your right hand term and take the highest power and multiply the first coefficent by it. Next you move to the term right next to it and subtract one from the n power. Thats you right hand side. Next is your left hand side. All you do is the exact same just start at the right side and move to the left. After you have expanded simplify and you have your answers simple right. 
Here is an example. 

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