Question

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

• A. $27$
• B. $7$
• C. $47$
• D. $37$

Answer 1

Answer: (D)

$37$

$\frac{1}{(1-3x)(1-4x)}$

$=(1-3x{)}^{-1}(1-4x{)}^{-1}$

$=\{1+(-1\left)\right(-3x)+\frac{(-1)(-1-1)}{2!}(-3x{)}^2+.......\}$$\{1+(-1\left)\right(-4x)+\frac{(-1)(-1-1)}{2!}(-4x{)}^2+.......\}$ [Expanding them in binomial series.]

$=\{1+3x+9x^2+....\}$$\{1+4x+16x^2+....\}$.

From above expansion of the series we get, the co-efficient of $x^2$

$=12+9+16=37$