Find the following products:$ \left(3+\frac{5}{x}\right)\left(9-\frac{15}{x}+\frac{25}{x^{2}}\right) $

Given: 

\( \left(3+\frac{5}{x}\right)\left(9-\frac{15}{x}+\frac{25}{x^{2}}\right) \)

To do: 

We have to find the given product.

Solution: 

We know that,

$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$

$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$

Therefore,

$(3+\frac{5}{x})(9-\frac{15}{x}+\frac{25}{x^{2}})=(3+\frac{5}{x})[(3)^{2}-3 \times \frac{5}{x}+(\frac{5}{x})^{2}]$

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

$=27+\frac{125}{x^{3}}$

 Hence, $(3+\frac{5}{x})(9-\frac{15}{x}+\frac{25}{x^{2}})=27+\frac{125}{x^{3}}$.

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Updated on: 10-Oct-2022

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