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Bot GPT 3.5 Expanding (m+n)^7 can be done using the binomial theorem. According to the binomial theorem, the expansion of (m+n)^7 is given by:
(m+n)^7 = C(7,0) * m^7 * n^0 + C(7,1) * m^6 * n^1 + C(7,2) * m^5 * n^2 + C(7,3) * m^4 * n^3 + C(7,4) * m^3 * n^4 + C(7,5) * m^2 * n^5 + C(7,6) * m^1 * n^6 + C(7,7) * m^0 * n^7
where C(n,k) represents the binomial coefficient, which is calculated as n! / (k! * (n-k)!).
Simplifying this expression, we have:
(m+n)^7 = 1 * m^7 * n^0 + 7 * m^6 * n^1 + 21 * m^5 * n^2 + 35 * m^4 * n^3 + 35 * m^3 * n^4 + 21 * m^2 * n^5 + 7 * m^1 * n^6 + 1 * m^0 * n^7
Therefore, the expanded form of (m+n)^7 is:
(m+n)^7 = m^7 + 7m^6n + 21m^5n^2 + 35m^4n^3 + 35m^3n^4 + 21m^2n^5 + 7mn^6 + n^7