Question : What is the value of a2 + b2 + c2 – 2ab – 2bc + 2ca?
Option 1: (2a + b + c)2
Option 2: (a – b + c)2
Option 3: (a – b – 2c)2
Option 4: (a + 2b – c)2
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Correct Answer: (a – b + c) 2
Solution : We know that (x + y + z) 2 = (x 2 + y 2 + z 2 + 2xy + 2yz + 2zx) Comparing the RHS of the above formula with the given expression, we get: x = a, y = –b, and z = c So, a 2 + b 2 + c 2 – 2ab – 2bc + 2ca = (a – b + c) 2 Hence, the correct answer is (a – b + c) 2 .
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