Factorize:
(a-b+c)²+(b-c+a)²+2(a-b+c)(b-c+a)
Answers
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.
HOPE THIS ANSWER WILL HELP YOU…..
Similar questions :
Factorize:
a²+2ab+b²-c²
https://brainly.in/question/15898064
Factorize:
X²-y²-4xz+4z²
https://brainly.in/question/15898065
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