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

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Question 778725: Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7


The Rth term of %28A%2BB%29%5EN is given by
this expression:

%28matrix%282%2C1%2CN%2CR-1%29%29A%5E%28N-R%2B1%29B%5E%28R-1%29

where %28matrix%282%2C1%2Cp%2Cq%29%29 means the same as C%28p%2Cq%29 or pCq 

In your problem A=m, B=2p, N=7, R=6

So we substitute those and get

%28matrix%282%2C1%2C7%2C6-1%29%29m%5E%287-6%2B1%29%282p%29%5E%286-1%29

%28matrix%282%2C1%2C7%2C5%29%29m%5E2%282p%29%5E5

%2821%29m%5E2%282%5E5p%5E5%29

21m%5E2%2A32%2Ap%5E5

672m%5E2p%5E5
Edwin