26) If ab is negative, which of the following CANNOT be negative? b-a a-b a^2b ab^2 a^2b^2

Given that ab is negative, we need to determine which of the following expressions cannot be negative.

Let's analyze each option:

1. $$b-a$$ : This expression represents the difference between b and a. Since ab is negative, it means that either a or b is negative. Therefore, the value of $$b-a$$ can be either positive or negative depending on the values of a and b.

2. $$a-b$$ : This expression represents the difference between a and b. Since ab is negative, it means that either a or b is negative. Therefore, the value of $$a-b$$ can be either positive or negative depending on the values of a and b.

3. $$a^{2}b$$ : This expression represents the product of the square of a and b. Since a^2 is always non-negative (positive or zero), and ab is negative, the value of $$a^{2}b$$ will always be negative.

4. $$ab^{2}$$ : This expression represents the product of ab and b^2. Since b^2 is always non-negative (positive or zero), and ab is negative, the value of $$ab^{2}$$ will always be negative.

5. $$a^{2}b^{2}$$ : This expression represents the product of the squares of a and b. Since both a^2 and b^2 are always non-negative (positive or zero), and ab is negative, the value of $$a^{2}b^{2}$$ will always be positive.

Based on the analysis, the expression that cannot be negative is $$a^{2}b^{2}$$ .