a^2+ab-b^2-a-2b
=(2a^2+2ab-2b^2-2a-4b)/2
=[(a^2+2ab+b^2)+(a^2-2a+1)-(3b^2+4b)-1]/2
=[(a+b)^2+(a-1)^2-3(b+2/3)^2+1/3]/2