Q. 165.0( 1 Vote )

Factorize: a2 – b2 + 2bc – c2.

Answer :

In the expression a2 – b2 + 2bc – c2, observe that the last three terms form:- (b – c)2.


a2 – b2 + 2bc – c2 = a2 – (b – c)2


We have the identity x2 – y2 = (x + y)(x – y)


a2 – b2 + 2bc – c2 = [a + (b – c)][a – (b – c)]


a2 – b2 + 2bc – c2 = (a + b – c)(a – b + c)


Hence, the factors of a2 – b2 + 2bc – c2 are (a + b – c) and (a – b + c).


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