Factorize each of the following expressions:$x^3 - 8y^3 + 27z^3 + 18xyz$

Given:

$x^3 - 8y^3 + 27z^3 + 18xyz$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

Therefore,

$x^3 - 8y^3 + 27z^3 + 18xyz = (x)^3 + (-2y)^3 + (3z)^3 - 3 \times x \times (-2y) \times (3 z)$

$= (x - y + 3z) (x^2 + 4y^2 + 9z^2 + 2xy + 6yz - 3zx)$

Hence, $x^3 - 8y^3 + 27z^3 + 18xyz = (x - y + 3z) (x^2 + 4y^2 + 9z^2 + 2xy + 6yz - 3zx)$.

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Updated on: 10-Oct-2022

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