Factorise: $9 a^{2} - 12 a b + 4 b^{2} - 9 m^{2} + 6 m n - n^{2}$

(- 3 a - 2 b - 3 m - n) (3 a + 2 b - 3 m + n)

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(3 a + 2 b + 3 m - n) (3 a - 2 b + 3 m + n)

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(3 a - 2 b + 3 m - n) (3 a - 2 b - 3 m + n)

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none of the above

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Solution

The correct option is C $(3 a - 2 b + 3 m - n) (3 a - 2 b - 3 m + n)$
$9 a^{2} - 12 a b + 4 b^{2} - 9 m^{2} + 6 m n - n^{2}$
$= 9 a^{2} - 12 a b + 4 b^{2} - (9 m^{2} - 6 m n + n^{2})$
$= (3 a - 2 b)^{2} - (3 m - n)^{2}$
$= (3 a - 2 b + 3 m - n) (3 a - 2 b - 3 m + n)$

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