Question

The coefficient of $x^{160}$ in the expansion of $(x^8+1{)}^{60}{(x^{12}+3x^4+\frac{3}{x^4}+\frac{1}{x^{12}})}^{-10}$ is

• A. ${}^{30}{C}_5$
• B. ${}^{30}{C}_6$
• C. ${}^{30}{C}_{23}$
• D. ${}^{30}{C}_{26}$

Answer 1

The correct option is A ${}^{30}{C}_5$

$\Rightarrow (x^8+1{)}^{60}{(x^4+\frac{1}{x^4})}^{-30}$
$\Rightarrow \frac{(x^8+1{)}^{60}(x^8+1{)}^{-30}}{x^{-120}}$
$\Rightarrow x^{120}(x^8+1{)}^{30}$
Now coeff. of $x^{160}{=}^{30}{C}_5$