Factorize each of the following expressions:$ \frac{x^{3}}{216}-8 y^{3} $

Given:

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

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

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

$=(\frac{x}{6}-2 y)[(\frac{x}{6})^{2}+\frac{x}{6} \times 2 y+(2 y)^{2}]$

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

Hence, $\frac{x^{3}}{216}-8 y^{3}=(\frac{x}{6}-2 y)(\frac{x^{2}}{36}+\frac{x y}{3}+4 y^{2})$.

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Updated on: 10-Oct-2022

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