Factorize the following expression : \(\frac{x^3}{216} – 8y^3\)
\[
\frac{x^3}{216} – 8y^3
\]
\[
= \left(\frac{x}{6}\right)^3 – (2y)^3
\]
\[
= \left(\frac{x}{6} – 2y\right)
\left[\left(\frac{x}{6}\right)^2 + \left(\frac{x}{6}\right)(2y) + (2y)^2\right]
\]
\[
= \left(\frac{x}{6} – 2y\right)
\left(\frac{x^2}{36} + \frac{xy}{3} + 4y^2\right)
\]