How do you find the 9th term in the expansion of the binomial (10x-3y)^12?

1 Answer
Feb 16, 2017

T_9=32476950000x^4y^8.

Explanation:

In the Expansion of Binomial (a+b)^n, the General (r+1)^(th) Term

is given by, T_(r+1)=""_nC_ra^(n-r)b^r" where, "r=0,1,2,...n.

In our Problem,

a=10x, b=-3y, n=12, and, r+1=9, i.e., r=8.

:. T_9=""_12C_8(10x)^(12-8)(-3y)^8

=""_12C_4(10)^4(3)^8x^4y^8,

={(12)(11)(10)(9)}/{(1)(2)(3)(4)}(10000)(6561)x^4y^8

=(11)(5)(9)(10000)(6561)x^4y^8

T_9=32476950000x^4y^8

Enjoy Maths.!