Answer :

In the expression a^{2} – b^{2} + 2bc – c^{2}, observe that the last three terms form:- (b – c)^{2}.

⇒ a^{2} – b^{2} + 2bc – c^{2} = a^{2} – (b – c)^{2}

We have the identity x^{2} – y^{2} = (x + y)(x – y)

⇒ a^{2} – b^{2} + 2bc – c^{2} = [a + (b – c)][a – (b – c)]

∴ a^{2} – b^{2} + 2bc – c^{2} = (a + b – c)(a – b + c)

Hence, the factors of a^{2} – b^{2} + 2bc – c^{2} are (a + b – c) and (a – b + c).

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