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  4. The number of different terms in the expansion of (1 - x)201(1 + x + x2)200 is

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Q. The number of different terms in the expansion of $\left(1 - x\right)^{201}\left(1 + x + x^{2}\right)^{200}$ is

NTA AbhyasNTA Abhyas 2020Binomial Theorem

Solution:

$(1-x)\left(1-x^{3}\right)^{200}$
$(1-x)\left[{ }^{200} C_{0}-{ }^{200} C_{1} x^{3}+\ldots \ldots \ldots \ldots\right]$
So, number of required terms $=2 \times 201=402$