Binomial Theorem And Its Simple Applications Question 51
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 $
BETA
