SOLUTION: Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7. Thanks

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Question 42556: Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7.
Thanks
Answer by psbhowmick(465) About Me  (Show Source):
You can put this solution on YOUR website!
The r-th term in the binomial expansion of %28a+%2B+x%29%5En for positive integral values of 'n' is given by t%5Br%5D+=+nC%5Br%5D%2Aa%5E%28n-r%29%2Ax%5Er.

Here, a = m, x = 2p, n = 7.
For the 6th term, r = 6.
So replace a, x, n and r in the formula of r-th term and get
t%5B6%5D+=+7C%5B6%5D%2Am%5E%287-6%29%2A%282a%29%5E6
or t%5B6%5D+=+2%5E6%2A7C%5B6%5D%2Am%5E1a%5E6

Now, 7C%5B6%5D+=+7%21%2F%286%21%287-6%29%21%29 = 7%21%2F%286%211%21%29 = %286%21%2A7%29%2F%286%21%2A1%29 = 7.

Hence the reqd 6th term is t%5B6%5D+=+2%5E6%2A7%2Ama%5E6 = 64%2A7%2Ama%5E6 = 448ma%5E6.