Factorize the following expression : \( \frac{1}{27}x^3 – y^3 + 125z^3 + 5xyz \)
\[
\frac{1}{27}x^3 – y^3 + 125z^3 + 5xyz
\]
\[
= \left(\frac{x}{3}\right)^3 + (-y)^3 + (5z)^3
– 3\left(\frac{x}{3}\right)(-y)(5z)
\]
\[
= \left(\frac{x}{3} – y + 5z\right)
\left[
\frac{x^2}{9} + y^2 + 25z^2
+ \frac{xy}{3} + 5yz – \frac{5xz}{3}
\right]
\]