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Question
Factorize a2 - b2 + 2bc - c2
Solution
= a2 - (b2 - 2bc + c2 )
Using identity a2 - 2ab + b2 = (a - b)2
= a2 - (b - c)2
Using identity a2 - b2 = (a + b)(a - b)
= (a + b - c)(a - (b - c))
= (a + b - c)(a - b + c)
∴ a2 - b2 + 2bc - c2 = (a + b - c)(a - b + c)
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