Product of expansions

Questions asking for the constant term in a product of two or more expressions, where at least one is a binomial expansion, requiring combination of terms from different factors.

3 questions

CAIE P1 2022 March Q3
3 Find the term independent of \(x\) in each of the following expansions.
  1. \(\left( 3 x + \frac { 2 } { x ^ { 2 } } \right) ^ { 6 }\)
  2. \(\left( 3 x + \frac { 2 } { x ^ { 2 } } \right) ^ { 6 } \left( 1 - x ^ { 3 } \right)\)
CAIE P1 2024 November Q4
4 Find the term independent of \(x\) in the expansion of each of the following:
  1. \(\left( x + \frac { 3 } { x ^ { 2 } } \right) ^ { 6 }\)
  2. \(\left( 4 x ^ { 3 } - 5 \right) \left( x + \frac { 3 } { x ^ { 2 } } \right) ^ { 6 }\) .
CAIE P1 2016 June Q4
4 Find the term that is independent of \(x\) in the expansion of
  1. \(\left( x - \frac { 2 } { x } \right) ^ { 6 }\),
  2. \(\left( 2 + \frac { 3 } { x ^ { 2 } } \right) \left( x - \frac { 2 } { x } \right) ^ { 6 }\).