Question 983041
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+b+c}}};
Second polynomial factor:  {{{a-b+c}}};


Factor a {{{-1}}} from part of the second polynomial factor,
{{{(a+b-c)(a-(b-c))}}}


Indicate a grouping in the first polynomial factor,
{{{(a+(b-c))(a-(b-c))}}}


Recognize a form leading to <b>Difference Of Squares</b>, although a little more complicated than what you usually find:
The multiplication is recognizably  {{{a^2-(b-c)^2}}}. 


The resulting multiplication of that is not likely a well-recognized form.
It becomes  {{{a^2-b^2+2bc-c^2}}}.