SOLUTION: I need help writing a binomial expansion for this expression... (m+n^2)^4 Thank you in advance to anyone that can help me.

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Question 127358This question is from textbook
: I need help writing a binomial expansion for this expression...
(m+n^2)^4
Thank you in advance to anyone that can help me.
This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

To reduce confusion, let p=n%5E2.

So the problem becomes %28m%2Bp%29%5E4

Write out the first 5 rows of Pascal's triangle (rows 0 through 4):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

The last row gives us the coefficients.
The exponent on m will start at 4 and decrease by one each term,
and the exponent on p will start at 0 and increase by 1 each term.

m%5E4p%5E0%2B4m%5E3p%5E1%2B6m%5E2p%5E2%2B4m%5E1p%5E3%2Bm%5E0p%5E4
m%5E4%2B4m%5E3p%2B6m%5E2p%5E2%2B4mp%5E3%2Bp%5E4

Now go back and replace p with n%5E2

m%5E4%2B4m%5E3n%5E2%2B6m%5E2n%5E4%2B4mn%5E6%2Bn%5E8