Factorise:
$8 x^{3} - 27 y^{3}$

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Solution

We know the identity $a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$

Using the above identity, the equation $8 x^{3} - 27 y^{3}$ can be factorised as follows:

$8 x^{3} - 27 y^{3} = (2 x)^{3} - {(3 y)}^{3} = (2 x - 3 y) [(2 x)^{2} + {(3 y)}^{2} + (2 x \times 3 y)] = (2 x - 3 y) (4 x^{2} + 9 y^{2} + 6 x y)$

Hence, $8 x^{3} - 27 y^{3} = (2 x - 3 y) (4 x^{2} + 9 y^{2} + 6 x y)$

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a^{3} + b^{3} + c^{3} - 3 a b c = \frac{1}{2} (a + b + c) [{(a - b)}^{2} + {(b - c)}^{2} + {(c - a)}^{2}]

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