"For both of column A and B, "a" and "b" are nonzero integers:"
Column A: (a+b)^2
Column B: (a^2 + b^2)
Please explain why the answer is: "The relationship cannot be determined from the information given."
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Alright, what are we suppose to find, integers a & b?
Those are given information, but what's the actual question about those two columns?
Sorry, I guess I should have put this: "Please explain why the answer for both columns is: "The relationship cannot be determined from the information given."
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The question just wants you to figure out the relationships between Column A and Column B.
I tried plugging numbers in for "a" and "b", and the answer seemed to be that the quantity in Column A was greater, but maybe it's only greater for some values?
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.
Aha! That makes tons of sense! Thank you so much! I REALLY, REALLY appreciate it! :)