Factorise: $8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$

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Solution

We have, $8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2}$
$= (2 a)^{3} - (b)^{3} - [3 \times {(2 a)}^{2} (b)] + [3 \times (2 a) \times b^{2}]$
Here, $x = 2 a, y = b$
$= {(2 a - b)}^{3}$ [Using the identity, $(x^{3} - y^{3} - 3 x^{2} y + 3 x y^{2}) = (x - y)^{3}$ ]

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