SOLUTION: If a+b = c prove by direct substitution that a^4 + b ^4+ c^4-2b^2c^2-2c^2a^2-2a^2b^2 = 0

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Question 53521: If a+b = c prove by direct substitution that
a^4 + b ^4+ c^4-2b^2c^2-2c^2a^2-2a^2b^2 = 0
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is easy to get lost doing, so I broke it up into smaller problems and then grouped all my like terms vertically in a table. Unfortunately, I can't put tables into my responses. Hopefully, I can be organized enough that you don't get lost.
First, substitute (a+b) everywhere that you have a c in the problem.
a%5E4%2Bb%5E4%2Bc%5E4-2b%5E2c%5E2-2c%5E2a%5E2-2a%5E2b%5E2=0
a%5E4%2Bb%5E4%2B%28a%2Bb%29%5E4-2b%5E2%28a%2Bb%29%5E2-2%28a%2Bb%29%5E2a%5E2-2a%5E2b%5E2=0
This is where I broke the problem up into smaller problems:
%28a%2Bb%29%5E2=%28a%2Bb%29%28a%2Bb%29
%28a%2Bb%29%5E2=a%5E2%2Bab%2Bab%2Bb%5E2
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
---------------------------
If you don't know the formula for this you can just distribute:
%28a%2Bb%29%5E4=%28a%2Bb%29%5E2%28a%2Bb%29%5E2
%28a%2Bb%29%5E4=%28a%5E2%2B2ab%2Bb%5E2%29%28a%5E2%2B2ab%2Bb%5E2%29



%28a%2Bb%29%5E4=a%5E4%2B4a%5E3b%2B6a%5E2b%5E2%2B4ab%5E3%2Bb%5E4
-------------------------------------
Substitute those back into the problem and you have:



0a%5E4%2B0b%5E4%2B0a%5E3b%2B0a%5E2b%5E2%2B0ab%5E3=0
0=0
I hope I caught all of my type-0's. Happy studying!