Factories: $8 x^{3} + y^{3} + 27 z^{3} - 18 x y z$

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Solution

We know that,
$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)$

For,
$8 x^{3} + y^{3} + 27 z^{3} - 18 x y z$

Let $a = 2 x, b = y, c = 3 z$

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

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8 x^{3} + y^{3} + 27 z^{3} - 18 x y z

Factorize $x^{3} - 8 y^{3} + 27 z^{3} + 18 x y z$

x^{3} - 8 y^{3} + 27 z^{3} + 18 x y z

8 x^{3} + y^{3}

16 (x + y)^{3} - 27

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