Home
Class 12
MATHS
Find the coefficient of x^7 in the expan...

Find the coefficient of `x^7` in the expansion of `(1+3x-2x^3)^(10)dot`

Text Solution

Verified by Experts

Coefficient of ` x^(7)` in the expansion of `(1 + 3x - 2x^(3))^(10)` is
`=sum (10!)/(alpha ! beta ! gamma !)(1)^(alpha) (3)^(beta)(-2)^(gamma)`
where , ` alpha + beta + gamma = 10 and beta + 3gamma = 7`
The possible values of ` alpha , beta " and" gamma ` are given below

`therefore ` Coefficient of `x^(7)`
`= (10!)/(3!7!0!) (1)^(3) (3)^(7) (-2)^(0) + (10!)/(5! 4!1!) (1)^(5) (3)^(4) (-2)^(1) + (10!)/(7!1!2!) (1)^(7) (3)^(1)-(-2)^(2)`
` = 262440 - 204120 + 4320 = 62640` .
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the coefficient of x in the expansion of (1-3x+7x^(2))(1-x)^(16)

Find the coefficient of x^6 y^3 in the expansion of (x+2y)^9 .

Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(11)

Find the coefficient of x^(15) in the expansion (x-x^(2))^(10)

Find the coefficient of x^5 in (x+3)^8

Find the coefficient of 1/(x^(17)) in the expansion (x^(4)-1/(x^(3)))^(15)

If the coefficient of x^(7) in the expansion of (ax^(2) +1/(bx))^(11) is equal to the coefficient of x^(-7) in the expansion of (ax- 1/(bx^(2)))^(11) are equal then prove that ab = 1 .

The coeficient of (x^(7)y^(3)) in the expansion of (x-y)^(10)- the coefficient of (x^(3)y^(7)) in the expansion of (x-y)^(10) is ………

Find the term independent of x in the expansion of (3x-2/(x^(2)))^(15)

Find the coefficient of x^(2) in the expansion of e^(2x+3) as a series in powers of x.