Factorise completely
\[\begin{equation*}
(x+y)^6 - (x-y)^6.
\end{equation*}\]

Can we factorise simpler things? \(6=2\times3\), so how about thinking about \(a^2-b^2\)? Or \(a^3 - b^3\)? Or even \(a^3 + b^3\)?

Or else we might wonder if, while it’s usually a bad idea, it’s worth trying to expand…