Question 1198624
i believe it's selection B which is 36x^2y^7


the general formula is (x + y) ^ n = sum (c(n,k) * x^(n-k) * y^k) from k = 0 to n.


each term is c(n,k) * x^(n-k) * y^k


when n = 9, .....


the first term is c(9,0) * x^9 * y^0
the second term is c(9,1) * x^8 * y^1
the third term is c(9,2) * x^7 * y^2
the fourth term is c(9,3) * x^6 * y^3
the fifth term is c(9,4) * x^5 * y^4
the sixth term is c(9,5) * x^4 * y^5
the seventh term is c(9,6) * x^3 * y^6
the eighth term is c(9,7) * x^2 * y^7
the 9th term is c(9,8) * x^1 * y^8
the 10th term is c(9,9) * x^0 * y^9


you are looking for the seventh term.


that term is c(9,6) * x^3 * y^6


c(9,6) = 9! / (6! * 3!) = (9*8*7*6!) = (6!*3!) = (9*8*7)/(3*2*1) = 84


the seventh term is therefore 84 * x^3 * y^6.


that would be selection A.


i confirmed with an online calculator.


the results of that calculator are shown below:


<img src = "http://theo.x10hosting.com/2022/112704.jpg">


the terms are what's between the + signs.


the seventh term is therefore equal to 84x^3y^6