Factorise the following:
$2 m^{2} + 19 m n + 30 n^{2}$

(2 m + 15 n) (m + 2 n)

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(m + 5 n) (m - 2 n)

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(2 m + 15 n) (m - 2 n)

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(m + 2 n) (m + 2 n)

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Solution

The correct option is A $(2 m + 15 n) (m + 2 n)$
$2 m^{2} + 19 m n + 30 n^{2}$
$= 2 m^{2} + 15 m n + 4 m n + 30 n^{2}$
$= 2 m^{2} + 4 m n + 15 m n + 30 n^{2}$
$= 2 m (m + 2 n) + 15 n (m + 2 n)$
$= (m + 2 n) (2 m + 15 n)$

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