Question

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

•2

•3

•5

•6

Answer 1

The correct option is 6

Explanation:

Given expression,

`(2m-3n)^9`

By the binomial expansion,

`(a+b)^x = \sum _(r=0)^(x) ^xC_r a^(x-r) b^(r)`

Where,

`^xC_r=(x!)/(r!(x-r)!)`

Thus,

`(2m-3n)^9 = \sum _(r=0)^(9) ^9C_r (2m)^(9-r) (-3n)^(r)`

For finding the term containing
`m^3`

9 - r = 3

⇒ 9 - 3 = r

⇒ r = 6

i.e. the required term is,

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

Hence, the power of n in that term = 6.