Expand the following, Using suitable identities
${(x - \frac{2}{3} y)}^{3}$

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Solution

${(x - \frac{2 y}{3})}^{3}$ is of the form ${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$

$= x^{3} - {(\frac{2 y}{3})}^{3} - 3 \times x \times \frac{2 y}{3} (x - \frac{2 y}{3})$

$= x^{3} - \frac{8 y^{3}}{27} - 2 x^{2} y + \frac{4 x y^{2}}{3}$

$= x^{3} - \frac{8 y^{3}}{27} + \frac{4 x y^{2}}{3} - 2 x^{2} y$

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