Factorize: $x^{2} - m^{2} + 6 m n - 9 n^{2}$

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Solution

$x^{2} - (m^{2} - 6 m n + 9 n^{2}) = x^{2} - [m^{2} - 2 (m) (3 n) + (3 n)^{2}] = x^{2} - (m - 3 n)^{2} = [x - (m - 3 n)] [x + (m - 3 n)] = (x - m + 3 n) (x + m - 3 n)$

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