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Division of Polynomials

Factorise : ...

Question

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

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

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

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

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

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Solution

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

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