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  4. The number of terms in the expansion of (1 + 2x + x2)20 when expanded in descending powers of x, is

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Q. The number of terms in the expansion of $(1 + 2x + x^2)^{20}$ when expanded in descending powers of x, is

Binomial Theorem

Solution:

We have
$(1 + 2x + x^2)20 = ((1 + x)^2)^{20} = (1 + x)^{40}$
$\therefore $ total no. of terms in the expansion $= 40 + 1=41$