Single binomial expansion

Questions asking for the constant term in a single binomial expansion of the form (ax^p + b/x^q)^n.

14 questions · Moderate -0.3

1.04a Binomial expansion: (a+b)^n for positive integer n
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CAIE P1 2014 June Q3
4 marks Moderate -0.8
3 Find the term independent of \(x\) in the expansion of \(\left( 4 x ^ { 3 } + \frac { 1 } { 2 x } \right) ^ { 8 }\).
CAIE P1 2016 June Q1
3 marks Moderate -0.5
1 Find the term independent of \(x\) in the expansion of \(\left( x - \frac { 3 } { 2 x } \right) ^ { 6 }\).
CAIE P1 2002 November Q1
3 marks Moderate -0.8
1 Find the value of the term which is independent of \(x\) in the expansion of \(\left( x + \frac { 3 } { x } \right) ^ { 4 }\).
CAIE P1 2010 November Q1
3 marks Moderate -0.3
1 Find the term independent of \(x\) in the expansion of \(\left( x - \frac { 1 } { x ^ { 2 } } \right) ^ { 9 }\).
CAIE P1 2011 November Q1
3 marks Moderate -0.3
1 Find the term independent of \(x\) in the expansion of \(\left( 2 x + \frac { 1 } { x ^ { 2 } } \right) ^ { 6 }\).
CAIE P1 2016 November Q2
4 marks Moderate -0.3
2 Find the term independent of \(x\) in the expansion of \(\left( 2 x + \frac { 1 } { 2 x ^ { 3 } } \right) ^ { 8 }\).
CAIE P1 2017 November Q1
4 marks Moderate -0.3
1 Find the term independent of \(x\) in the expansion of \(\left( 2 x - \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 9 }\).
CAIE P1 2019 November Q1
3 marks Moderate -0.3
1 Find the term independent of \(x\) in the expansion of \(\left( 2 x + \frac { 1 } { 4 x ^ { 2 } } \right) ^ { 6 }\).
OCR MEI C1 Q3
3 marks Moderate -0.3
3 Find the term independent of \(x\) in the expansion of \(\left( x - \frac { 2 } { x } \right) ^ { 4 }\).
OCR MEI C1 Q4
4 marks Standard +0.3
4 The binomial expansion of \(\left( 2 x + \frac { 5 } { x } \right) ^ { 6 }\) has a term which is a constant. Find this term.
OCR MEI C1 2013 January Q6
4 marks Moderate -0.3
6 The binomial expansion of \(\left( 2 x + \frac { 5 } { x } \right) ^ { 6 }\) has a term which is a constant. Find this term.
OCR MEI Paper 3 2018 June Q6
2 marks Moderate -0.3
6 Find the constant term in the expansion of \(\left( x ^ { 2 } + \frac { 1 } { x } \right) ^ { 15 }\).
AQA Paper 3 2021 June Q4
5 marks Moderate -0.8
  1. Show that the first three terms, in descending powers of \(x\), of the expansion of $$(2x - 3)^{10}$$ are given by $$1024x^{10} + px^9 + qx^8$$ where \(p\) and \(q\) are integers to be found. [3 marks]
  2. Find the constant term in the expansion of $$\left(2x - \frac{3}{x}\right)^{10}$$ [2 marks]
SPS SPS FM 2025 October Q5
4 marks Standard +0.3
In this question you must show detailed reasoning. Consider the expansion of \(\left(\frac{x^2}{2} + \frac{a}{x}\right)^6\). The constant term is 960. Find the possible values of \(a\). [4]