Factorise: $10 a^{3} - 11 a^{2} b - 8 a b^{2}$

a (2 a + b) (5 a - 8 b)

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a (2 a + b) (5 a + 8 b)

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a (2 a - b) (5 a - 8 b)

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a (2 a + b) (5 a - 8 b)

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Solution

The correct option is A $a (2 a + b) (5 a - 8 b)$
In the given expression, common term has to be separated:
Thus, $10 a^{3} - 11 a^{2} b - 8 a b^{2}$ becomes $a (10 a^{2} - 11 a b - 8 b^{2})$
By middle term splitting we can write the above expression as:
$a (10 a^{2} - 16 a b + 5 a b - 8 b^{2})$
which further becomes $a (2 a (5 a - 8 b) + b (5 a - 8 b))$
On Further simplification it becomes; $a (2 a + b) (5 a - 8 b)$
So, the correct answer is option (a).

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