Question

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

Answer 1

The expression is given as : (a – b + c)² + (b – c + a)² + 2(a – b + c) (b – c + a)

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

By using an  identity: x² + y² + 2xy = (x + y)² , where x = a - (b - c), y = a + (b - c)] :  

= [(a - (b - c)) + (a + (b - c))]²

= [a - b + c + a + b - c]²

= (2a)²

= 4a²

Hence,  the factorisation of (a – b + c)² + (b – c + a)² + 2(a – b + c) (b – c + a) is 4a².

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Answer 2

Question:

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

Answer: 4a²

Step by Step explanation:-

Identity to be used:

(a + b+c)² = a² + b² + c² + 2ab + 2ac + 2ca

On solving it with the same identity, we get:

=> a² + b² + c² - 2ab + 2ca - 2bc + b² + c² + a² - 2bc - 2ac + 2ab + 2(ab - ac + a² - b² - c² + 2bc)

=> a² + b² + c² - 2ab + 2ca - 2bc + b² + c² + a² - 2bc - 2ac + 2ab + 2a² - 2b² - 2c² + 4bc

=> 4a²

Thus, the anwer is 4a²