Question

How do you find the seventh term of `(x+y)^12`?

Answer 1

`(12!)/(6!*6!)*x^6y^6.`

Explanation:

If we expand `(x+y)^n,` in the descending powers of `x`, the General

`(r+1)^(th)` Term, denoted by `T_(r+1),` is given by,

`T_(r+1)=""_nC_rx^(n-r)y^r, r=0,1,2,..,n.`

In our Problem, `n=12, and, r=6,` giving,

`T_7=""_12C_6x^(12-6)y^6=(12!)/(6!*6!)*x^6y^6.`