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# The total no. of terms in the expansion $(x+y)^{100}+(x-y)^{100}$ is ?

$\begin{array}{1 1} 50 \\ 51 \\ 101 \\ 202 \end{array}$

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Toolbox:
• The expansion of $(x+y)^n$ has $n+1$ terms
$(x+y)^{100}$ and $(x-y)^{100}$ have 101 terms each
In the expansion of $(x+y)^{100}+(x-y)^{100}$,
$2^{nd},4^{th},6^{th}.$..............terms get cancelled (total 50 terms) and
$1^{st},3^{rd}$.......... terms (total 51 terms) are added twice.
$\therefore$ no. of terms left over in the expansion = 51
answered Sep 15, 2013

No. Of terms = 51