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

Options

A. `-272`
B. `-540`
C. `-870`
D. `-918`

Answer

D

Explanation

`((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`