Factorize the following expression : \( 27x^3 – y^3 – z^3 – 9xyz \)
\[
27x^3 – y^3 – z^3 – 9xyz
\]
\[
= (3x)^3 + (-y)^3 + (-z)^3 – 3(3x)(-y)(-z)
\]
\[
= \left[(3x) + (-y) + (-z)\right]
\left[
(3x)^2 + (-y)^2 + (-z)^2
– (3x)(-y) – (-y)(-z) – (-z)(3x)
\right]
\]
\[
= (3x – y – z)
(9x^2 + y^2 + z^2 + 3xy – yz + 3xz)
\]