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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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