There is no "ax", that is atimesx^2! Have you considered applying thedefinitionof "harmonic" to ax^2+ bxy+ cy^2? What is ? Whatisthe definition of "harmonic"?

Again, what is the2. Show that if v is harmonic conjugate of u in a domain D, then uv is harmonic in D.

(lost me)definitionof "harmonic conjugate"? If you don't know, you had better look up those definitions. Certainly your teacher expects to know those definitions!