SOLUTION: quantitative comparison which is greater col a: 4x^2 + 4y^2 col b: (2x + 2y)^2 please show how you get the answer...thanks

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Question 982704: quantitative comparison
which is greater
col a: 4x^2 + 4y^2
col b: (2x + 2y)^2
please show how you get the answer...thanks

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Expand column b.
%282x%2B2y%29%5E2=4%28x%2By%29%5E2=4%28x%5E2%2B2xy%2By%5E2%29=4x%5E2%2B4y%5E2%2B8xy=A%2B8xy
where A is the value column A.
Which is greater depends on the value of x and y.
If x=y=0, then they are equal.
If x%3E0 and y%3C0, then
4x%5E2%2B4y%5E2%3E%282x%2B2y%29%5E2
Similarly if x%3C0 and y%3E0,
4x%5E2%2B4y%5E2%3E%282x%2B2y%29%5E2
And finally if x%3E0 and y%3E0,
4x%5E2%2B4y%5E2%3C%282x%2B2y%29%5E2