Factorize:
$125 x^{3} + 27 y^{3} + 8 z^{3} - 90 x y z$

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Solution

$125 x^{3} + 27 y^{3} + {8 z}^{3} - 90 x y z {(5 x)}^{3} + {(3 y)}^{3} + {(2 z)}^{3} - 5 x .3 y .2 z \times 3 a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a) (5 x + 3 y + 2 z) (25 x^{2} + 9 y^{2} + 4 z^{2} - 15 x y - 6 y z - 10 x z)$

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Factorize $125 x^{3} - 27 y^{3} - 225 x^{2} y + 135 x y^{2}$

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