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

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Solution

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

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