Question

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

Answer 1

Answer:

4a²

Step-by-step explanation:

(a-b+c)²+(b-c+a)²+2(a-b+c)(b-c+a)

= [(a-b+c)+(b-c+a)]²

/* By algebraic identity:

x²+y²+2xy = (x+y)² */

= (a-b+c+b-c+a)²

= (2a)²

= 4a²

Therefore,

(a-b+c)²+(b-c+a)²+2(a-b+c)(b-c+a)= 4a²

•••♪

Answer 2

4a²

Step-by-step explanation:

Given,

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

Applying the formula: a² + b² + 2ab = (a + b)²

[(a - b + c) + (b - c + a)]²

Adding both the expressions:

(a - b + c + b - c + a)²

Subtracting b:

(a + c - c + a)²

Subtracting c:

(a + a)²

Adding a:

(2a)²

2a × 2a

4a²

Learn more:

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