If we expand out the expression for column A, we get:
a^2 + 2ab + b^2
This has all the same terms as the second column, but then the extra 2ab.
Now, when a and b are both greater than 0, column A is always greater than column B because 2ab is always positive, so it's always going to have an extra bit added to it.
If a or b is negative and the other positive, then the "2ab" becomes a subtraction and so column A is now becoming less than column B.
Then lastly, if both a and b are negative, then "2ab" is still positive and column A is once again greater than column B.