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

$\begin{array}{1 1}(A)\;50\\(B)\;202\\(C)\;51\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $(a+b)^n=nC_0a^n+nC_1a^{n-1}b^1+nC_2a^{n-2}b^2+.....nC_ra^{n-r} b^r+nC_n b^n$
$(x+a)^{100}+(x-a)^{100}$
$2[100C_0 x^{100}a^0+100C_2 x^{98}a^2+.....+100C_{100}x^0a^{100}]$
$\Rightarrow 2x^{100}+2^{100}C_2x^{98}a^2+....2a^{100}$
Hence there are 51 terms.
Hence (C) is the correct answer.