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

always non-positive, either 0 or negative

neither, if a=b = 0, then ab-a^2-b^2 = 0

if a=b, then ab-a^2-b^2 = a^2-a^2-b^2 = -b^2 <0 for any b value

negative for any other a, b values

a b ab -a^2-b^2 ab-a^2-b^2

1 2 2 -1-4 2-5 = -3

2 3 6 -4-9 6-13 = -7

1/4 1/2 1/8 -1/16-1/4 1/8-5/16 = -3/16

-1 -2 2 -2 -4 2-6 = -4

-1 2 -2 -1-4 -2-5 = -7

always negative or zero

compare with 2ab -a^2 -b^2 which factored = -(a-b)^2 which is always negative as anything squared is always >0. put a negative sign in front and it's always non-positive