Binomial expansion with reciprocals

Expand expressions of the form (x + k/x)^n where both x and 1/x terms appear in the binomial.

4 questions · Moderate -0.8

1.04a Binomial expansion: (a+b)^n for positive integer n
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OCR MEI C1 Q10
4 marks Easy -1.2
10 Find the binomial expansion of \(\left( x + \frac { 5 } { x } \right) ^ { 3 }\), simplifying the terms.
OCR C2 2007 June Q2
5 marks Easy -1.2
2 Expand \(\left( x + \frac { 2 } { x } \right) ^ { 4 }\) completely, simplifying the terms.
OCR MEI C1 2010 January Q8
4 marks Easy -1.2
8 Find the binomial expansion of \(\left( x + \frac { 5 } { x } \right) ^ { 3 }\), simplifying the terms.
Edexcel C2 Q2
8 marks Standard +0.3
For the binomial expansion, in descending powers of \(x\), of \(\left( x^3 - \frac{1}{2x} \right)^{12}\),
  1. find the first 4 terms, simplifying each term. [5]
  2. Find, in its simplest form, the term independent of \(x\) in this expansion. [3]