# The number of terms in the expansion of (x + y + z)n ______. - Mathematics

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The number of terms in the expansion of (x + y + z)n ______.

#### Solution

The number of terms in the expansion of (x + y + z)n ((n + 1)(n + 2))/2.

Explanation:

The expression (x + y + z)n can be written a [x + (y + z)]n

∴ [x + y + z]n = nC0xn (y + z)0 + nC1(x)n–1 (y + z) + nC2(x) n–2(y + z)2 + … + nCn(y + z)n

∴ Number of terms 1 + 2 + 3 + 4 + … (n + 1)

= ((n + 1)(n + 2))/2

Concept: Binomial Theorem for Positive Integral Indices
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 26 | Page 145
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