How to solve this math question?

Question

How to solve this calculation and determine from the result whether it is positive or negative?

ab-a²-b²

Thank you!

Answer 1

ab -a^2 -b^2

= -(a^2 + b^2 -ab)

= -(a^2 -2ab +b^2 +ab)

=-(a^2 -2ab +b^2) - ab

= -(a-b)^2 -ab

(a-b)^2 is always positive or zero always non negative

-(a-b)^2 is always negative or zero, always non positive

ab is positive if a and b are the same sign, either both positive or both negative

-ab is negative if a and b are the same sign

ab is negative if a and b are the opposite sign

-ab is positive if a and b are the opposite sign

-(a-b)^2-ab is always negative if if a and b are the same sign

and indeterminate if a and b are opposite signs

and always zero if a and b are both zero