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Binomial Expansion: Number of Terms
publish date: 2026/05/23 05:43:43.946082 UTC
volume_mute
When expanding \((x + y)^n\) using the Binomial Theorem (where \(n\) is a natural number), how many terms does the expansion contain?
Correct Answer
\(n + 1\) terms
Explanation
The binomial expansion \((x+y)^n = {}^nC_0 x^n + {}^nC_1 x^{n-1}y + \cdots + {}^nC_n y^n\) contains exactly \((n+1)\) terms. In each term, the sum of the indices of \(x\) and \(y\) equals \(n\).
Reference
Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012