Add a square + 3ab - bc,b square+3bc - ca , and c square + 3ca - ab
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Required sum =a
2
+3ab−bc+b
2
+3bc−ca+c
2
+3ca−ab
Collecting like terms,
=a
2
+b
2
+c
2
+3ab−ab+3bc−bc+3ca−ca
=a
2
+b
2
+c
2
+2ab+2bc+2ca
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