Binomial Expansions   \((n \in \mathbb{N})\)

Unit: Sequences and Series

Flipped Learning: Binomial Expansions   \((n \in \mathbb{N})\)

DFM Key skill:

  • Binomial expansion of \((ax \pm b)^n\), where \(n\) is a positive integer."
  • Determine the value of a coefficient in a binomial expansion with a positive integer power.

Task Commentary

This is a new topic for most students. However, given the procedural nature of most basic questions on this topic, it lends itself well to independent study. Students generally have no trouble performing basic binomial expansions or finding coefficients with minimal or no teacher input.

Following this task, a brief starter to practise the skills is usually enough to refresh students’ memories and enable the starting point for the topic to be much further advanced.

The topic is introduced such that students initially perform binomial expansions using Pascal’s triangle, before advancing onto using the formula to find expansions where the power is sufficient large that using Pascal’s triangle would be an inefficient method.