Question

The total number of terms in the expansion of ${\left((1+x^{2/3})(1+x^{4/3}-x^{2/3})\right)}^{2021}$ is

• A. $4043$
• B. $3033$
• C. $2022$
• D. $2021$

Answer 1

The correct option is C $2022$

Given : ${\left(\right(1+x^{2/3}\left)\right(1+x^{4/3}-x^{2/3}\left)\right)}^{2021}$
Let $a=1$ and $b=x^{2/3}$
Then the expression becomes
${\left(\right(a+b\left)\right(a^2+b^2-ab\left)\right)}^{2021}$
$=(a^3+b^3{)}^{2021}$
$=(1+x^2{)}^{2021}$
$\therefore$ Total number of terms $=2021+1=2022$