Q. The coefficient of $x^{n}$ in the expansion of $(1 + x)(1 - {x)}^{n}$ is
A) $(n - 1)$
B) $( - 1)^{n}(1 - n)$
C) ${( - 1)}^{n - 1}{(n - 1)}^{2}$
D) ${( - 1)}^{n - 1}n$
Explanation
(b)
The coefficient of $x^{n}$ in the expansion of $(1 + x)(1 - {x)}^{n}$
$= coefficient\ of\ x^{n}\ in\ (1 - {x)}^{n} + The\ coefficient\ of\ x^{n - 1\ }\ in\ (1 - {x)}^{n}$
$= ( - 1)^{n}\frac{n!}{n!0!} + ( - 1)^{n - 1}\frac{n!}{1!(n - 1)!}$
$= ( - 1)^{n}(1 - n)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.