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.

37 questions · Easy -1.0

CAIE P1 2012 November Q1
Moderate -0.8
1 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 2 - \frac { 1 } { 2 } x \right) ^ { 7 }\).
Edexcel P2 2024 January Q2
Moderate -0.8
  1. Find the coefficient of the term in \(x ^ { 7 }\) of the binomial expansion of
$$\left( \frac { 3 } { 8 } + 4 x \right) ^ { 12 }$$ giving your answer in simplest form.
OCR MEI C1 2008 January Q7
Easy -1.3
7
  1. Find the value of \({ } ^ { 8 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(\left( 1 - \frac { 1 } { 2 } x \right) ^ { 8 }\).
OCR MEI C1 2009 January Q5
Easy -1.2
5
  1. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)\).
  2. Find the coefficient of \(x ^ { 2 }\) in the binomial expansion of \(( 1 + 2 x ) ^ { 7 }\).
OCR MEI C1 2007 June Q6
Moderate -0.8
6 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 2008 June Q8
Moderate -0.8
8 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 5 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q6
Moderate -0.8
6 Find the coefficient of \(x ^ { 2 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q3
Moderate -0.8
3 Find the term which has the highest coefficient in the expansion of \(( 1 + x ) ^ { 8 }\).
OCR MEI C1 Q2
Moderate -0.8
2 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 7 }\).
OCR MEI C1 Q3
Moderate -0.8
3 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 2 - 4 x ) ^ { 5 }\).
OCR MEI C1 Q5
Easy -1.2
5
  1. Evaluate \({ } ^ { 5 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q6
Moderate -0.8
6 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 6 }\).
OCR MEI C1 Q12
Easy -1.2
12
  1. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)\).
  2. Find the coefficient of \(x ^ { 2 }\) in the binomial expansion of \(( 1 + 2 x ) ^ { 7 }\).
OCR MEI C1 Q13
Moderate -0.8
13 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 5 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q14
Easy -1.2
14
  1. Find the value of \({ } ^ { 8 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(\left( 1 - \frac { 1 } { 2 } x \right) ^ { 8 }\).
OCR MEI C1 Q15
Moderate -0.8
15 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 Q16
Easy -1.2
16 Calculate the coefficient of \(x ^ { 4 }\) in the expansion of \(( x + 5 ) ^ { 6 }\).
OCR MEI C1 Q17
Easy -1.2
17 Calculate \({ } ^ { 6 } \mathrm { C } _ { 3 }\).
Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 2 x ) ^ { 6 }\).
OCR MEI C1 2007 January Q5
Easy -1.2
5 Calculate the coefficient of \(x ^ { 4 }\) in the expansion of \(( x + 5 ) ^ { 6 }\).
OCR MEI C1 2011 June Q5
Easy -1.2
5 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 6 }\).
OCR MEI C1 2012 June Q6
Easy -1.2
6
  1. Evaluate \({ } ^ { 5 } \mathrm { C } _ { 3 }\).
  2. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 5 }\).
OCR MEI C1 2013 June Q6
Easy -1.2
6 Find the coefficient of \(x ^ { 3 }\) in the binomial expansion of \(( 2 - 4 x ) ^ { 5 }\).
OCR MEI C1 2014 June Q7
Moderate -0.8
7 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( 5 + 2 x ) ^ { 7 }\).
OCR MEI C1 Q4
Moderate -0.8
4 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 2 + 3 x ) ^ { 5 }\).
OCR PURE 2022 May Q1
Moderate -0.8
1 Find the term in \(x ^ { 3 }\) in the binomial expansion of \(( 3 - 2 x ) ^ { 5 }\).