Factorise: $x^{2} + 9 y^{2} - 25 m^{2} - 16 n^{2} + 6 x y + 40 m n$ .

(2 x + 3 y + 5 m + 4 m) (x - 3 y - 2 m + 4 n)

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(2 x + 3 y + 4 m - 4 m) (x + 3 y - 5 m - 4 n)

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(x + 3 y + 5 m - 4 n) (x + 3 y - 5 m + 4 n)

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(x + y + 3 m - 4 m) (x + 3 y - + 5 m + 4 n)

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Solution

The correct option is C $(x + 3 y + 5 m - 4 n) (x + 3 y - 5 m + 4 n)$
$x^{2} + 9 y^{2} - 25 m^{2} - 16 n^{2} + 6 x y + 40 m n$
$= x^{2} + 6 x y + 9 y^{2} - 25 m^{2} + 40 m n - 16 n^{2}$
$= (x^{2} + 6 x y + 9 y^{2}) - (25 m^{2} - 40 m n + 16 n^{2})$
$= (x + 3 y)^{2} - (5 m - 4 n)^{2}$
$= [(x + 3 y) + (5 m - 4 n)] [(x + 3 y) - (5 m - 4 n)]$
$= (x + 3 y + 5 m - 4 n) (x + 3 y - 5 m + 4 n)$

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