SOLUTION: WHAT KIND OF SPECIAL PRODUCT IS (A+B-C)(A-B+C)

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Question 983041: WHAT KIND OF SPECIAL PRODUCT IS (A+B-C)(A-B+C)
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
One must examine the shown expression and think about what can be done and understood, maybe for a few seconds; or maybe for a few minutes.


After thinking a while,...

I'm using lower case variables instead of upper case.

First polynomial factor: a%2Bb%2Bc;
Second polynomial factor: a-b%2Bc;

Factor a -1 from part of the second polynomial factor,
%28a%2Bb-c%29%28a-%28b-c%29%29

Indicate a grouping in the first polynomial factor,
%28a%2B%28b-c%29%29%28a-%28b-c%29%29

Recognize a form leading to Difference Of Squares, although a little more complicated than what you usually find:
The multiplication is recognizably a%5E2-%28b-c%29%5E2.

The resulting multiplication of that is not likely a well-recognized form.
It becomes a%5E2-b%5E2%2B2bc-c%5E2.