SOLUTION: find the fifth term of the binomial expansion (x+y)^7

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Question 1144258: find the fifth term of the binomial expansion (x+y)^7
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

1-st term is  C%5B7%5D%5E0%2Ax%5E%287-0%29%2Ay%5E0 = x%5E7.


2-nd term is  C%5B7%5D%5E1%2Ax%5E%287-1%29%2Ay%5E1 = C%5B7%5D%5E1%2Ax%5E6%2Ay.


3-rd term is  C%5B7%5D%5E2%2Ax%5E%287-2%29%2Ay%5E2 = C%5B7%5D%5E2%2Ax%5E5%2Ay%5E2.


4-th term is  C%5B7%5D%5E3%2Ax%5E%287-3%29%2Ay%5E3 = C%5B7%5D%5E3%2Ax%5E4%2Ay%5E3.


5-th term is  C%5B7%5D%5E4%2Ax%5E%287-4%29%2Ay%5E4 = C%5B7%5D%5E4%2Ax%5E3%2Ay%5E4.     ANSWER


See the lesson
    - Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic
"Binomial expansion, binomial coefficients, Pascal's triangle".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the fifth term of the binomial expansion (x+y)^7
=====================
Pascal's Triangle is reasonable for the 7th power:
1    2    1
1    3    3    1
1    4    6    4    1
1    5   10   10    5    1
1    6   15   20   15    6    1
1    7   21   35   35   21    7    1

---------------
The coefficient is 35
---> 35x%5E3y%5E4
===================================
I could have started at 1 4 6 4 1 since I know 11^4 = 14641.
I wouldn't use Pascal's Triangle for exponents greater than 8 or 9, unless directed to do so.