factorise a2-b2-c2+2bc
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=a² - (b-c)²
=(a-(b-c))(a+(b-c)) [ using identity a²-b² =(a-b). (a+b) ]
= (a-b+c)(a+b-c)
hence.,a²-b²+2bc - c² = (a-b+c)(a+b-c)
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a^2-b^2-c^2+2bc
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a+b-c)(a-b+c)