Expand : ${(3 x - \frac{5}{x})}^{3}$

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Solution

Given : ${(3 x - \frac{5}{x})}^{3}$
According to the equation,
$(a + b)^{3} = a^{3} + b^{3} + 3 b (a + b)$
we get,
It can written as

${(3 x - \frac{5}{x})}^{3}$ $= (3 x)^{3} - {(\frac{5}{x})}^{3} - 3 (3 x) (\frac{5}{x}) (3 x - \frac{5}{x})$
On further calculation we get,

${(3 x - \frac{5}{x})}^{3}$ $= 27 x^{3} - {(\frac{125}{x})}^{3} - 45 (3 x - \frac{5}{x})$

${(3 x - \frac{5}{x})}^{3}$ $= 27 x^{3} - {(\frac{125}{x})}^{3} - 135 x + \frac{225}{x}$

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