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  4. The number of terms in the expansion of (1 + x)101 (1 + x2 - x)100 in powers of x is :

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

JEE MainJEE Main 2014Binomial Theorem

Solution:

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 × 101 = 202 $ terms