SOLUTION: how can you foil (a+b+c)(a+b+c) ?

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Question 338934: how can you foil (a+b+c)(a+b+c) ?
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution.
Let D=b%2Bc.
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=%28a%2BD%29%28a%2BD%29
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2BaD%2BDa%2BD%5E2
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2B2aD%2BD%5E2
Now substitute back,
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2Ba%28b%2Bc%29%2B%28b%2Bc%29a%2B%28b%2Bc%29%5E2
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2Bab%2Bac%2Bab%2Bac%2Bb%5E2%2B2bc%2Bc%5E2
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2Bb%5E2%2Bc%5E2%2B2ab%2B2ac%2B2bc
%28a%2Bb%2Bc%29%28a%2Bb%2Bc%29=a%5E2%2Bb%5E2%2Bc%5E2%2B2%28ab%2Bbc%2Bac%29