Factorise
${12 y}^{3} + {6 a}^{3}$

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Solution

$12 y^{3} + 6 a^{3}$
$= 6 (2 y^{3} + a^{3})$
$= 6 ({\sqrt[3]{2} y}^{3} + a^{3})$ is of the form $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$= 6 (\sqrt[3]{2} y + a) ({(\sqrt[3]{2} y)}^{2} + a^{2} - \sqrt[3]{2} y a)$
$= 6 (y \sqrt[3]{2} + a) (y^{2} 2^{\frac{2}{3}} + a^{2} - a y 2^{\frac{1}{3}})$

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6 a^{3}, - 4 a^{3}, 10 a^{3}, - 8 a^{3}

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