Binomial with negative or fractional powers of x

Questions asking for a coefficient in the expansion of expressions like (x + k/x^m)^n or (kx^p + m/x^q)^n, requiring careful tracking of powers when terms contain x in denominators or non-unit powers.

14 questions

CAIE P1 2003 June Q1
1 Find the value of the coefficient of \(\frac { 1 } { x }\) in the expansion of \(\left( 2 x - \frac { 1 } { x } \right) ^ { 5 }\).
CAIE P1 2011 June Q1
1 Find the coefficient of \(x\) in the expansion of \(\left( x + \frac { 2 } { x ^ { 2 } } \right) ^ { 7 }\).
CAIE P1 2012 June Q2
2 Find the coefficient of \(x ^ { 6 }\) in the expansion of \(\left( 2 x ^ { 3 } - \frac { 1 } { x ^ { 2 } } \right) ^ { 7 }\).
CAIE P1 2014 June Q1
1 Find the coefficient of \(x\) in the expansion of \(\left( x ^ { 2 } - \frac { 2 } { x } \right) ^ { 5 }\).
CAIE P1 2016 June Q1
1 Find the coefficient of \(x\) in the expansion of \(\left( \frac { 1 } { x } + 3 x ^ { 2 } \right) ^ { 5 }\).
CAIE P1 2018 June Q2
2 Find the coefficient of \(\frac { 1 } { x }\) in the expansion of \(\left( x - \frac { 2 } { x } \right) ^ { 5 }\).
CAIE P1 2019 June Q1
1 Find the coefficient of \(x\) in the expansion of \(\left( \frac { 2 } { x } - 3 x \right) ^ { 5 }\).
CAIE P1 2004 November Q1
1 Find the coefficient of \(x\) in the expansion of \(\left( 3 x - \frac { 2 } { x } \right) ^ { 5 }\).
CAIE P1 2006 November Q1
1 Find the coefficient of \(x ^ { 2 }\) in the expansion of \(\left( x + \frac { 2 } { x } \right) ^ { 6 }\).
CAIE P1 2008 November Q1
1 Find the value of the coefficient of \(x ^ { 2 }\) in the expansion of \(\left( \frac { x } { 2 } + \frac { 2 } { x } \right) ^ { 6 }\).
CAIE P1 2015 November Q2
2 Find the coefficient of \(x\) in the expansion of \(\left( \frac { x } { 3 } + \frac { 9 } { x ^ { 2 } } \right) ^ { 7 }\).
CAIE P1 2018 November Q1
1 Find the coefficient of \(\frac { 1 } { x ^ { 2 } }\) in the expansion of \(\left( 3 x + \frac { 2 } { 3 x ^ { 2 } } \right) ^ { 7 }\).
CAIE P1 2018 November Q1
1 Find the coefficient of \(\frac { 1 } { x ^ { 3 } }\) in the expansion of \(\left( x - \frac { 2 } { x } \right) ^ { 7 }\).
AQA Paper 2 2020 June Q3
3 Find the coefficient of \(x ^ { 2 }\) in the binomial expansion of \(\left( 2 x - \frac { 3 } { x } \right) ^ { 8 }\)