Factorize each of the following expressions: x^3/216 - 8y^3

Question

Factorize each of the following expressions:

\(\frac{\text{x}^{3}}{216}-8\text{y}^{3}\)

Answer 1

Given,

\(\frac{\text{x}^{3}}{216}-8\text{y}^{3}=(\frac{\text{x}}{6})^{3}\,-(2\text{y})^{3}\)

= \((\frac{\text{x}}{6}-2\text{y})(\frac{\text{x}^{2}}{36}+4\text{y}^{2}+\frac{\text{xy}}{3})\)