What is the coefficient of x^7 in the expansion of (3 - x)^(11)?

Question

What is the coefficient of
`x^7` in the expansion of
`(3 - x)^(11)`?

Answer 1

-26730

Step-by-step explanation:

To find the coefficient of
`x^7` in the expansion of
`(3 -x)^(11)`

Use Binomial Expansion:

`(x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^(n-1) y + \ ^n C_2 x^(n-2)y^2 + ...+ \ ^n C_n y^n`

In this expansion,

`(3-x)^(11)`

The coefficient of
`x^7`

`= 11C_(7) (3)^(11-7) (-x)^7`

`= (330) (81) (-x^7)`

`= -26730x^7`