Factorize each of the following expressions:$27x^3 - y^3 - z^3 - 9xyz$

Given:

$27x^3 - y^3 - z^3 - 9xyz$

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,

$27x^3-y^3-z^3-9xyz = (3x)^3 + (-y)^3 + (-z)^3 - 3 \times 3x \times (-y) \times (-z)$

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

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

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

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Updated on: 10-Oct-2022

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