Question

Need help with this ASAP​

Answer 1

Given:

`(3x-2)^9`

To find:

The coefficient of
`x^6` in the expansion of
`(3x-2)^9`.

Solution:

We know that, in the expansion of
`(x+y)^n`,

`T_(r+1)=^nC_rx^(n-r)y^r` ...(i)

`(3x-2)^9` has only one x and in
`x^6`, the power of x is 6. It is possible if

`n-r=6`

`9-r=6`

`9-6=r`

`3=r`

Putting n=9, r=3, x=3x and y=-2 in (i), we get

`T_(3+1)=^9C_3(3x)^(9-3)(-2)^3`

`T_(4)=(9!)/(3!(9-3)!)* (3x)^(6)(-8)`

`T_(4)=(9* 8* 7* 6!)/(3* 2* 1* (9-3)!)* (729x^(6))(-8)`

`T_(4)=84* (729)* (-8)* x^(6)`

`T_(4)=-489888x^6`

Therefore, the coefficient of
`x^6` in the expansion of
`(3x-2)^9` is -489888.