Factorize each of the following expressions:$8x^3 + 27y^3 - 216z^3 + 108xyz$

Given:

$8x^3 + 27y^3 - 216z^3 + 108xyz$

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,

$8x^3 + 27y^3 - 216z^3 + 108xyz = (2x)^3 + (3y)^3 + (6z)^3 - 3 \times (2x) \times (3y) \times (-6z)$

$= (2x + 3y - 6z) [(2x)^2 + (3y)^2 + (-6z)^2 - 2x \times 3y - 3y \times (-6z) - (-6z) \times 2x]$

$= (2x + 3y - 6z) (4x^2 + 9y^2 + 36z^2 - 6xy + 18yz + 12zx)$

Hence, $8x^3 + 27y^3 - 216z^3 + 108xyz = (2x + 3y - 6z) (4x^2 + 9y^2 + 36z^2 - 6xy + 18yz + 12zx)$.

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Updated on: 10-Oct-2022

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