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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