Factorize:

$a^{2} - b^{2} + 2 b c - c^{2}$

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Solution

$a^{2} - b^{2} + 2 b c - c^{2} = a^{2} - (b^{2} - 2 b c + c^{2}) {∵ a^{2} + b^{2} - 2 a b = (a - b)^{2}} = a^{2} - (b - c)^{2} = (a)^{2} - (b - c)^{2} {∵ a^{2} - b^{2} = (a + b) (a - b)} = (a + b - c) (a - b + c)$

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\frac{a^{2} - b^{2} - 2 b c - c^{2}}{a^{2} + b^{2} + 2 a b - c^{2}}

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