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Taking Out Common Factors

Factorise: ...

Question

Factorise: $8 x^{3} - 2 x^{2} y - 15 x y^{2}$

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Solution

The given expression $8 x^{3} - 2 x^{2} y - 15 x y^{2}$ can be factorised as follows:

$8 x^{3} - 2 x^{2} y - 15 x y^{2} = x (8 x^{2} - 2 x y - 15 y^{2}) = x (8 x^{2} - 12 x y + 10 x y - 15 y^{2}) = x [4 x (2 x - 3 y) + 5 y (2 x - 3 y)]$
$= x (4 x + 5 y) (2 x - 3 y)$

Hence, $8 x^{3} - 2 x^{2} y - 15 x y^{2} = x (4 x + 5 y) (2 x - 3 y)$

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