Seventh Day!

Hi guys it's me Gaby! I hope you all did an awesome job on your quiz! If not then that's okay! Keep trying and studying so you do a great job on the next! The quiz was about solving for n. We first had to put it into the combination formula, we then expand the n!, we cancel out the same terms from the numerator and the denominator, then move all terms on one side equaling it to 0, then finally you factor the polynomial. You should get the roots of n=-8 and n=9. Then check by plugging in the roots and your answer should be n=9. Remember negative roots have to be rejected!

Anyways today we learned about the Binomial Theorem, or Pascal's Triangle. Honestly at first it was confusing, but after a while, hopefully everyone has a good understanding of it. 

Here's some methods for you so you can decipher with coefficient is the correct on by expanding different binomials:

The Tipi Method -  This basically shows a tipi shape by simply starting by #1 all the way down, diagonally to #9.

The Hockey Stick Method - Like in the picture above, the pink lines are shaped as a hockey stick. 1+3+6+10+15+21+28=84. All of those numbers going diagonally down towards the left, if you add them all together you get the sum of the number diagonally down towards the right. 

The Triangle Method - By choosing 2 numbers beside each other, you add them together and it should equal to the number right under the 2 numbers you added.