Question

The coefficient of $x^4$ in the expansion of $\frac{(1-3x{)}^2}{(1-2x)}$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

$4$

We need to find coefficient of $x^4$ in $\frac{(1-3x{)}^2}{(1-2x)}$

It can be expanded as $\frac{(1-3x{)}^2}{1-2x}=(1-3x{)}^2(1-2x{)}^{-1}$
$=(1-6x+9x^2)[1+2x+(2x{)}^2+.......]$
Therefore, coefficient of $x^4$ is $2^4-6\left(2^3\right)+9\left(2^2\right)$
$=16-48+36=4$