Question
Factorise: $\frac{\text{x}^3}{216}-8\text{y}^3$
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Answer
$\frac{\text{x}^3}{216}-8\text{y}^3$ $=\Big(\frac{\text{x}}{6}\Big)^3-(2\text{y})^3$ $=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\bigg[\Big(\frac{\text{x}}{6}\Big)^2+\Big(\frac{\text{x}}{6}\Big)(2\text{y})+(2\text{y})^2\bigg]$ $=\Big(\frac{\text{x}}{6}-2\text{y}\Big)\Big(\frac{\text{x}^2}{36}+\frac{\text{xy}}{3}+4\text{y}^2\Big)$
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