(1x+y3)^3 ⇒(1x)^3+(y3)^3+3(1x)(y3)(1x+y3) ⇒1x^3+y^327+yx(1x+y3x) ⇒1x^3+y^327+yx^2+y^23x . ...

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Exponential Representation for Irrational Numbers

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Question

Expand ${(\frac{1}{x} + \frac{y}{3})}^{3}$

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Solution

${(\frac{1}{x} + \frac{y}{3})}^{3}$
$\Rightarrow {(\frac{1}{x})}^{3} + {(\frac{y}{3})}^{3} + 3 (\frac{1}{x}) (\frac{y}{3}) (\frac{1}{x} + \frac{y}{3})$
$\Rightarrow \frac{1}{x^{3}} + \frac{y^{3}}{27} + \frac{y}{x} (\frac{1}{x} + \frac{y}{3 x})$
$\Rightarrow \frac{1}{x^{3}} + \frac{y^{3}}{27} + \frac{y}{x^{2}} + \frac{y^{2}}{3 x}$ .

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