Sometimes we have to go just a little bit further than expand a bracket using the binomial theorem. We may have two brackets multiplied together, both brackets raised to a power. We may have to expand the brackets up to the term in
for example. We do this by expanding each bracket using the binomial theorem, ignoring higher powers than
then multiplying the brackets, again ignoring higher powers than
Example: Expand
Nothing needs to be done to the first bracket but the second can be expanded to give
Now expand the brackets against each other.
This last expression simplifies to
hence
