Question

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

• A. $200$
• B. $201$
• C. $202$
• D. $402$

Answer 1

Answer: (D)

$(1-x){\left(1-x^3\right)}^{200}$
$(1-x)\left[{}^{200}{C}_0-{}^{200}{C}_1{x}^3+\dots \dots \dots \dots \right]$
So, number of required terms $=2\times 201=402$