Simplify(a+b+c)^2+(a-b-c)^2(a+b+c)^2-(a-b-c)^2
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QUESTION -
Simplify(a+b+c)^2+(a-b-c)^2(a+b+c)^2-(a-b-c)^2
ANSWER -
the given expression is:
(a+b+c)2+(a−b+c)2+(a+b−c)2=(a+b+c)2+[a−
(b−c)]2+[a+(b−c)]2=a2+b2+c2+2ab+2bc+2ca+a2+
(b−c)2−2a.(b−c)+a2+(b−c)2+2a.
(b−c)=3a2+b2+c2+2ab+2bc+2ca+2.
(b−c)2=3a2+b2+c2+2ab+2bc+2ca+2.
[b2+c2−2bc]=3a2+3b2+3c2+2ab+2bc+2ca−4bc=3a2+3b2+3c2+2ab−2bc+2ca
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