Question 42556
The r-th term in the binomial expansion of {{{(a + x)^n}}} for positive integral values of 'n' is given by {{{t[r] = nC[r]*a^(n-r)*x^r}}}.


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[6] = 7C[6]*m^(7-6)*(2a)^6}}}
or {{{t[6] = 2^6*7C[6]*m^1a^6}}}


Now, {{{7C[6] = 7!/(6!(7-6)!)}}} = {{{7!/(6!1!)}}} = {{{(6!*7)/(6!*1)}}} = 7.


Hence the reqd 6th term is {{{t[6] = 2^6*7*ma^6}}} = {{{64*7*ma^6}}} = {{{448ma^6}}}.