Q. The total number of terms in the expansion of ${(x + y)}^{100} + {(x - y)}^{100}$ after simplification is
A) 51
B) 202
C) 100
D) 50
Explanation
(a)
Let $f(x) = (x + y)^{100} + (x - y)^{100}$
Here, $n = 100$, which is even.
$\therefore$ Total number of terms
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{n + 2}{2} = \frac{100 + 2}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ = 51$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.