A) \[{{(a-b)}^{2}}-{{(b-c)}^{2}}+{{(c-a)}^{2}}\]
B) \[{{(a-b)}^{2}}+{{(b-c)}^{2}}-{{(c-a)}^{2}}\]
C) \[{{(a-b)}^{2}}-{{(b-c)}^{2}}-{{(c-a)}^{2}}\]
D) \[{{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}}\]
Correct Answer: D
Solution :
\[2{{a}^{2}}+2{{b}^{2}}+2{{c}^{2}}-2ab-2bc-2ca\] \[=\,({{a}^{2}}-2ab+{{b}^{2}})\,+\,({{b}^{2}}-2bc+{{c}^{2}})+\,({{c}^{2}}-2ca+{{a}^{2}})\] \[={{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}}\]
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