SOLUTION: (alpha-beta)^2=(alpha+beta)^2-4alphabeta Where does the 4 alphabeta come from?

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Question 970737: (alpha-beta)^2=(alpha+beta)^2-4alphabeta
Where does the 4 alphabeta come from?

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Use simpler symbols, like a and b.

%28a-b%29%5E2---------Do the multiplication and see what happens.

a%5E2-ab-ab%2Bb%5E2
a%5E2-2ab%2Bb%5E2, which is your left member.

What happens if you work from the right member using the same variable assignments?
%28a%2Bb%29%5E2-4ab
a%5E2%2B2ab%2Bb%5E2-4ab
a%5E2%2B2ab-4ab%2Bb%5E2
a%5E2-2ab%2Bb%5E2, which is the right member; and is the SAME result as when simplifying the left member.

We did not need to know where the 4ab, or 4*alpha*beta, came from. We just wanted to find out if the left and right members are equal. Yes, they are equal.