NDA 2025 Maths · Mathematics · Binomial Theorem · easy

The number of terms in the expansion of (x+y)^10+(x-y)^10 after simplification is

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The number of terms in the expansion of

(x+y)^{10}+(x-y)^{10}

after simplification is

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Answer: (C) $6$

Terms with odd powers of

y

cancel and those with even powers double:

2\left[x^{10}+\binom{10}{2}x^8y^2+\dots+y^{10}\right]

. The powers of

y

are

0,2,4,6,8,10

, giving

6

terms. The value

11

ignores the cancellation.

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