Question

The number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$ after simplification is

• A. $202$
• B. $101$
• C. $51$
• D. $50$

Answer 1

Answer: (C)

$51$

The first expansion i.e., ${(x+a)}^{100}$ has $101$ terms, and the next expansion i.e., ${(x-a)}^{100}$ also has $101$ terms

But the terms having odd powers of $x$ will get cancelled

So the remaining terms will be $\frac{102}{2}=51$, as the first terms of both the expansions do not get cancelled and the even ones will be twice in number.