Problems Involving the Binomial Expansion

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 infor example. We do this by expanding each bracket using the binomial theorem, ignoring higher powers thanthen 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 giveNow expand the brackets against each other.

This last expression simplifies to

hence