Chpt. 9.5: Expanding Binomials and Pascal's Triangle

There are many patterns within Pascal's Triangle. For example:
          -The Sum of Rows is equal to 2 to the power of that row.

20 = 1 21 = 1+1 = 2 22 = 1+2+1 = 4 23 = 1+3+3+1 = 8 24 = 1+4+6+4+1 = 16          -Another important pattern is the Hockey Stick Pattern: When adding up all of the numbers in a diagonal (leaving out the last number in the diagonal), the sum of those numbers will equal the last number of the diagonal.

1+6+21+56 = 84
1+7+28+84+210+462+924 = 1716
1+12 = 13

nCr

n= Row number (# of different items)

r= Diagonal (# of Combinations selected at a time) 

_{1.)To find 6}C_{4, you would go down the 6th row, and 4th diagonal and your answer would be 15.} 

₆C₄= 15

_{2.) Find 10}C₇.
  Plug it into the calculator.

Expanding Binomials

- The purpose of Pascal's Triangle is to help you expand binomials. It is where you find the binomial coefficients.

Solve.

-If the binomial is a subtraction, the signs of the expanded form alternate between +/-