Question

Factorize (a - b + c)² + (b - c + a)² + 2(a - b + c) (b - c + a)

Answer 1

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