Discussion
What is the number of terms in the given expression?
\(\left(x^{2} + \frac{2}{x}\right)^{11}\)
Answer: A
The expression has 12 terms. In the binomial expansion of \((a+b)^{n}\) there are \(n+1\) terms, because the power of \(a\) runs from \(n\) down to 0, which gives \(n+1\) different values. Here \(a = x^{2}\), \(b = \frac{2}{x}\) and \(n = 11\), so \[ \text{number of terms} = 11 + 1 = 12 \] The number 11 is the power and not the count of terms, while 22 and 24 come from doubling the power or the count, which does not follow from the binomial theorem.
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