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