Question

The number of terms in the expansion of $(1+x{)}^{101}(1+x^2-x{)}^{100}$ in powers of $x$ is :

• A. 302
• B. 301
• C. 202
• D. 101

Answer 1

Answer: (C)

Given expansion is
$(1+x{)}^{101}(1-x+x^2{)}^{100}$
$=(1+x)(1+x{)}^{100}(1-x+x^2{)}^{100}$
$=(1+x)[(1+x)(1-x+x^2{)}^{100}$
$=(1+x)[(1-x^3{)}^{100}]$
Expansion $(1-x^3{)}^{100}$ will have $100+1=101$ terms
So, $(1+x)(1-x^3{)}^{100}$ will have $2\times 101=202$ terms