Question

In the expansion of (2m-3n)^9 one of the terms contains m^3. Determine the exponent of n in this term

Answer 1

when you expand it, the exponents must add up to nine. so if m = 3, then n must = 6

Answer 2

6

Explanation:

We are given that
`(2m-3n)^9`

One of the terms contains
`m^3`

We have to find the exponent of n in this term.

By using binomial expansion

Binomial expansion

`(a+b)^n=nC_0a^nb^0+nC_1a^{n-1)b^1+nC_2a^(n-2)b^2+.....+nC_na^0b^n`

`(2m-3n)^9=9C_0(2m)^9+9C_1(2m)8(-3n)^1+9C_2(2m)^7(-3n)^2+9C_3(2m)^6(-3n)^3+9C_4(2m)^5(-3n)^4+9C_5(2m)^4(-3n)^5+9C_6(2m)^3(-3n)^6+9C_7(2m)^2(-3n)^7+9C_8(2m)(-3n)^8+9C_9(-3n)^9`

The term in which
`m^3` occur is given by

`9C_6(2m)^3(-3n)^6=9C_6(8m^3)(-3)^6n^6`

Hence, the exponent of n in this term =6