Question

In the expansion of ${\left(x-\frac{1}{x}\right)}^6$, the constant term is

• A. $-20$
• B. $20$
• C. $30$
• D. $-30$

Answer 1

The correct option is A $-20$

In expansion of ${(x-\frac{1}{6})}^6$, the constant term is ${}^6{c}_k{x}^{6-k}(\frac{-1}{x}{)}^k$

In constant term, power of $x$ must be zero

$\therefore 6-k-k=0$

$2k=6.$

$k=3$

Hence, the constant term is ${-}^6{c}_3=-20.$