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The coefficient of x^3 in the expansion ...

The coefficient of `x^3` in the expansion of `(3-2x)/((1+3x)^3)` is

A

`-272`

B

`-540`

C

`-870`

D

`-918`

Text Solution

Verified by Experts

The correct Answer is:
D
`((3-2x))/((1+3x)^(3))=(3-2x)(1+3x)^(-3)`
`=(3-2x)(1-9x+((-3)(-4))/(2!).9x^(2)+((-3)(-4)(-5))/(3!).27 x^(3)+....)`
`["Expanding"(1+3x)^(-3)]`
`=(3-2x)(1-9x+54x^(2)-270x^(3)+…..)`
`therefore" Coefficient of "x^(3)=-270xx3-2xx54`
`=-810-108=-918`
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Knowledge Check

  • The coefficient of x^(3) in the expansion of 3^(x) is

    A
    `(3^(3))/6`
    B
    `(log3)^(3)/3`
    C
    `(log(3)^(3))/6`
    D
    ` ((log3)^(3))/6`

  • The coefficient of x in the expansion of (x+3)^(3) is

    A
    1
    B
    9
    C
    18
    D
    27

  • The coefficient of x^2 in the expansion of (3x - (1)/( x) )^6 is-

    A
    405
    B
    1215
    C
    2430
    D
    3645

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