Expand the following :$(\frac{5x}{y} + \frac{y}{5x})^3$

Given :

The given expression is $(\frac{5x}{y} + \frac{y}{5x})^3$ 

To do :

We have to expand the given expression.

Solution :

We know that,

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

Therefore,

$(\frac{5x}{y} + \frac{y}{5x})^3 =  (\frac{5x}{y})^3 + (\frac{y}{5x})^3 +3(\frac{5x}{y})(\frac{y}{5x})(\frac{5x}{y} + \frac{y}{5x})$

                                                     $= 125(\frac{x}{y})^3 + \frac{1}{125}(\frac{y}{x})^3 + 3 (\frac{5x}{y} + \frac{y}{5x})$.

The expansion of $(\frac{5x}{y} + \frac{y}{5x})^3$  is $125(\frac{x}{y})^3 + \frac{1}{125}(\frac{y}{x})^3 + 3 (\frac{5x}{y} + \frac{y}{5x})$.

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Updated on: 10-Oct-2022

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