SOLUTION: Find the third term in the expansion of (2x-3y)^8

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Question 331217: Find the third term in the expansion of (2x-3y)^8


Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the third term in the expansion of %282x-3y%29%5E8 

The kth term in the expansion of %28A%2BB%29%5En is given
by the formula:

%28matrix%282%2C1%2Cn%2Cr-1%29%29%2AA%5E%28n-r%2B1%29%2AB%5E%28r-1%29 or sometimes it's written C%28n%2Cr-1%29%2AA%5E%28n-r%2B1%29%2AB%5E%28r-1%29

In your problem,

A=2x, B=-3y, n=8, r=3

So we substititute:

%28matrix%282%2C1%2C8%2C3-1%29%29%2A%282x%29%5E%288-3%2B1%29%2A%28-3y%29%5E%283-1%29 or C%288%2C3-1%29%2A%282x%29%5E%288-3%2B1%29%2A%28-3y%29%5E%283-1%29

%28matrix%282%2C1%2C8%2C2%29%29%2A%282x%29%5E6%2A%28-3y%29%5E2 or C%288%2C2%29%2A%282x%29%5E6%2A%28-3y%29%5E2

%28%288%2A7%29%2F%282%2A1%29%29%2A2%5E6%2Ax%5E6%2A%28-3%29%5E2y%5E2

%2856%2F2%29%2A64%2Ax%5E6%2A9y%5E2

28%2A64%2A9%2Ax%5E6%2Ay%5E2

16128x%5E6y%5E2

Edwin