Is this boolean expression reducible?
Yes, factor out the a2'. You should see something interesting with what happens to a1.

If you don't, post a comment and I can help further.

When you factor out a2', you get a2'(a1' + a1)

The statement a1' + a1 means (a1 or NOT a1). It should be obvious that this is ALWAYS true and thus can be removed from the logic statement. This leaves you with F1 = a2'

In general, the tools for reducing logic expressions that I know of are algebraic manipulation (deMorgan's Laws, distributive property, etc.), Karnaugh Maps, and the Quine McCluskey Algorithm.