Standard binomial expansion coefficient

Questions asking for a coefficient in the expansion of (a + bx)^n where both terms are simple powers of x (or constants), using the standard binomial theorem directly.

41 questions · Moderate -0.9

1.04a Binomial expansion: (a+b)^n for positive integer n
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OCR H240/02 2018 September Q6
9 marks Standard +0.3
6
  1. Find the coefficient of \(x ^ { 4 }\) in the expansion of \(( 3 x - 2 ) ^ { 10 }\).
  2. In the expansion of \(( 1 + 2 x ) ^ { n }\), where \(n\) is a positive integer, the coefficients of \(x ^ { 7 }\) and \(x ^ { 8 }\) are equal. Find the value of \(n\).
  3. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\frac { 1 } { \sqrt { 4 + x } }\).
AQA Paper 1 2023 June Q1
1 marks Easy -1.2
1 Find the coefficient of \(x ^ { 7 }\) in the expansion of \(( 2 x - 3 ) ^ { 7 }\) Circle your answer.
-2187-128 2128
Pre-U Pre-U 9794/1 2013 June Q2
4 marks Easy -1.2
2 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 2 x ) ^ { 5 }\).
WJEC Unit 1 2018 June Q18
Moderate -0.5
The coordinates of three points \(A , B , C\) are \(( 4,6 ) , ( - 3,5 )\) and \(( 5 , - 1 )\) respectively. a) Show that \(B \widehat { A C }\) is a right angle.
b) A circle passes through all three points \(A , B , C\). Determine the equation of the circle.
OCR MEI C1 Q4
4 marks Moderate -0.8
Find the coefficient of \(x^3\) in the expansion of \((2 + 3x)^5\). [4]
OCR MEI C1 2006 June Q8
4 marks Easy -1.2
Calculate \(^6C_3\). Find the coefficient of \(x^3\) in the expansion of \((1 - 2x)^6\). [4]
OCR MEI C1 2009 June Q5
4 marks Easy -1.3
  1. Calculate \(^5C_3\). [2]
  2. Find the coefficient of \(x^3\) in the expansion of \((1 + 2x)^5\). [2]
OCR MEI C1 2011 June Q5
4 marks Moderate -0.8
Find the coefficient of \(x^4\) in the binomial expansion of \((5 + 2x)^6\). [4]
OCR MEI C1 2012 June Q6
5 marks Moderate -0.8
  1. Evaluate \(^5C_3\). [1]
  2. Find the coefficient of \(x^3\) in the expansion of \((3 - 2x)^5\). [4]
OCR MEI C1 2013 June Q6
4 marks Moderate -0.8
Find the coefficient of \(x^3\) in the binomial expansion of \((2 - 4x)^5\). [4]
AQA AS Paper 1 2021 June Q1
1 marks Easy -1.8
Find the coefficient of the \(x\) term in the binomial expansion of \((3 + x)^4\) Circle your answer. [1 mark] 12 27 54 108
AQA AS Paper 1 2022 June Q3
3 marks Easy -1.2
Find the coefficient of the \(x^3\) term in the expansion of \(\left(3x + \frac{1}{2}\right)^4\) [3 marks]
AQA AS Paper 2 2020 June Q5
4 marks Standard +0.3
Joseph is expanding \((2 - 3x)^7\) in ascending powers of \(x\). He states that the coefficient of the fourth term is 15120 Joseph's teacher comments that his answer is almost correct. Using a suitable calculation, explain the teacher's comment. [4 marks]
AQA Paper 2 2018 June Q2
1 marks Easy -1.8
Find the coefficient of \(x^2\) in the expansion of \((1 + 2x)^7\) Circle your answer. [1 mark] 42 4 21 84
WJEC Unit 1 2019 June Q12
6 marks Moderate -0.3
In the binomial expansion of \((2 - 5x)^8\), find
  1. the number of terms, [1]
  2. the \(4^{\text{th}}\) term, when the expansion is in ascending powers of \(x\), [2]
  3. the greatest positive coefficient. [3]
SPS SPS FM 2019 Q2
3 marks Easy -1.2
Find the coefficient of the \(x^4\) term in \((2 - 3x)^6\). [3]