Binomial Theorem

Hello classmates, I am Reedhee Modha and I will be summarizing about what was covered during our morning class today. Mr. Paitek started, the first class with the quiz and we all had the same question for the first time, lesson reviewing expanding and simplifying the binomial from yesterday's class. And later on he taught us about basic exponent rules, Pascal's triangle and binomial theorem. 

Expand binomials as follows:

(x+y)0=[1]

=1

(x+y)1=[1]x1y0+[1]x0y1

=x+y

(x+y)2=[1]x2y0+[2]x1y1+[1]x0y2

=x2+2xy+y2

(x+y)3=[1]x3y0+[3]x2y1+[3]x1y2+[1]x0y3

=x3+3x2y+3xy2+y3

(x+y)4=[1]x4y0+[4]x3y1+[6]x2y2+[4]x1y3+[1]x0y4

=x4+4x3y+6x2y2+4xy3+y4

(x+y)5=[1]x5y0+[5]x4y1+[10]x3y2+[10]x2y3+[5]x1y4+[1]x0y5

=x5+5x4y+10x3y2+10x2y3+5xy4+y5

                                        
Pascal's Triangle

We note that the coefficients the numbers in front of each term follow a patter.

Here is the video that I found about Pascal's Triangle:

The Binomial Theorem:

Example: (2x – 5y)⁷

^{I'll plug 2x, -5y, and 7 into the Binomial theorem, counting up from zero to seven to get each term.}

^{Then simplify:}   

I hope this informations help you. Most importantly, our first test is next week on 24th Tuesday, good luck preparing for the test!!! 

-Reedhee Modha