This is a proof question that I just cannot get what's required for the life of me. This isn't part of my assessed homework, just fyi.

Suppose , , ..., is a random sample from a random variable which has expectation and variance . Consider the sample variance

Show that

We're also given the hint that may be written as and that . I've used both of these but I just can't seem to get at all. Closest I've gotten is