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Question
Factorize (a - b + c)2 + (b - c + a)2 + 2(a - b + c) (b - c + a)
Solution
Let (a - b + c) = x and (b - c + a ) = y
= x2 + y2 + 2xy
Using identity a2 + b2 + 2ab = (a + b)2
= ( x + y )2
Now, substituting x and y
= (a - b + c + b - c + a)2
Cancelling -b, +b and +c, -c
= (2a )2
= 4a2
∴ (a - b + c)2 + (b - c + a)2 + 2(a - b + c)(b - c + a ) = 4a2
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