Q. 123.9( 24 Votes )

Factorize:

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

Answer :

Given,


(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))


[Applying identity: x2 + y2 +2xy = (x + y)2 , where x= a-(b-c), y= a+(b-c)]


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

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