Factorise:
$9 - a^{2} + 2 a b - b^{2}$

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Solution

$9 - a^{2} + 2 a b - b^{2} = 9 - (a^{2} - 2 a b + b^{2}) = 3^{2} - (a - b)^{2} = [3 - (a - b)] [3 + (a - b)] = (3 - a + b) (3 + a - b)$

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