Factorise
$2 a^{3} + 16 b^{3} - 5 a - 10 b$

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Solution

Given Equation is $2 a^{3} + 16 b^{3} - 5 a - 10 b$

This can be written as

$2 (a^{3} + 8 b^{3}) - 5 a - 10 b$

We know that

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

$2 (a + 2 b) (a^{2} - 2 a b + 4 b^{2}) - 5 a - 10 b = 2 (a + 2 b) (a^{2} - 2 a b + 4 b^{2}) - 5 (a + 2 b) = (a + 2 b) (2 (a^{2} - 2 a b + 4 b^{2}) - 5) = (a + 2 b) (2 a^{2} - 4 a b + 8 b^{2} - 5)$

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