Binomial-Theorem-And-Its-Simple-Applications Question 215

Question: What is the coefficient of $ x^{3} $ in $ \frac{(3-2x)}{{{(1+3x)}^{3}}}? $

Options:

A) - 272

B) - 540

C) - 870

D) -918

Show Answer

Answer:

Correct Answer: D

Solution:

  • [d] $ \frac{(3-2x)}{{{(1+3x)}^{3}}}=(3-2x){{(1+3x)}^{-3}} $ $ =(3-2x)[1-9x+\frac{(-3)(-4)}{2!}.,9x^{2} $ $ +\frac{(-3)(-4)(-5)}{3!}.27x^{3}+….] $ [Expanding $ {{(1+3x)}^{-3}} $ ] $ =(3-2x)(1-9x+54x^{2}-270x^{3}+…..) $
    $ \therefore $ Coefficient of $ x^{3}=-270\times 3-2\times 54=-918 $

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