To simplify the given expression, we can combine like terms:
a^2 + b^2 + 4ab - 2ab = a^2 + b^2 + 2ab
Now, we need to determine the conditions under which this expression is greater than 0. We can factor out a common factor of a sum of squares:
(a + b)^2
For this expression to be greater than 0, the sum of squares must be greater than 0. In other words, the expression (a + b)^2 is positive whenever a and b are not both zero.
Therefore, the inequality a^2 + b^2 + 4ab - 2ab > 0 is satisfied for all real numbers a and b except when a = 0 and b = 0.
To simplify the given expression, we can combine like terms:
a^2 + b^2 + 4ab - 2ab
= a^2 + b^2 + 2ab
Now, we need to determine the conditions under which this expression is greater than 0. We can factor out a common factor of a sum of squares:
(a + b)^2
For this expression to be greater than 0, the sum of squares must be greater than 0. In other words, the expression (a + b)^2 is positive whenever a and b are not both zero.
Therefore, the inequality a^2 + b^2 + 4ab - 2ab > 0 is satisfied for all real numbers a and b except when a = 0 and b = 0.