$8 a^{3} - 2 a^{2} b - 15 a b^{2} =$

(4 a + 5 b) (2 a^{2} - 3 a b)

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(4 a - 5 b) (2 a^{2} - 3 a b)

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(4 a - 5 b) (2 a^{2} + 3 a b)

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(4 a + 5 b) (2 a^{2} + 3 a b)

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Solution

The correct option is A $(4 a + 5 b) (2 a^{2} - 3 a b)$
Lets factorise as follows,
$8 a^{3} - 2 a^{2} b - 15 a b^{2} = 8 a^{3} - 12 a^{2} b + 10 a^{2} b - 15 a b^{2}$
$= 4 a^{2} (2 a - 3 b) + 5 a b (2 a - 3 b)$
$= (4 a^{2} + 5 a b) (2 a - 3 b)$
$= a (4 a + 5 b) (2 a - 3 b)$
$= (4 a + 5 b) (2 a^{2} - 3 a b)$

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