SOLUTION: I need help with this question. What is the third term in the expansion of (x + 2y) power of 17?

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Question 715608: I need help with this question. What is the third term in the expansion of (x + 2y) power of 17?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
SInce the power is 17, the expansion would have 17%2B1=18 terms.
The degree of all the terms (the sum of the powers of x and of %282y%29 ) will be 17.
The first term will have x%5E17 and %282y%29%5E0.
The second term will have x%5E16 and %282y%29%5E1.
Term number 3 would have
%282y%29%5E%28%283-1%29%29=%282y%29%5E2=4y%5E2 as a factor.
As the power is 17 , it would also have
x%5E%28%2817-2%29%29=x%5E15 as a factor.
The other factor would be the combinatorial number that tells you how many different groups of 2 you can make with 17 different items:
%28matrix%282%2C1%2C17%2C2%29%29=17%2A16%2F1%2F2=136
The third term is
136%2Ax%5E15%2A4y%5E2=highlight%28544x%5E15y%5E2%29