Up until now the power ‘n’ was a positive integer. When the power is not a positive integer you can only use the formula

  • {(1 + a)}^n \equiv 1 + na + \dfrac{n(n - 1)}{{2!}}{a^2} + \dfrac{{n(n - 1)(n - 2)}}{{3!}}{a^3} + .....}

Examples in the video

Expand the following:

  1. \text{Expand}\hphantom{aa}\sqrt {(1 - 2x)} \hphantom{aa}\text{ up to the term in }{x^3}
  2. \text{Expand}\hphantom{aa}\dfrac{3}{{2 - x}} \hphantom{aa} \text{up to the term in }{x^2}