If $x = -2$ and $y = 1$, by using an identity find the value of the following:$ \left(5 y+\frac{15}{y}\right)\left(25 y^{2}-75+\frac{225}{y^{2}}\right) $

Given: 

$x = -2$ and $y = 1$

To do: 

We have to find the value of \( \left(5 y+\frac{15}{y}\right)\left(25 y^{2}-75+\frac{225}{y^{2}}\right) \).

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,

$(5 y+\frac{15}{y})(25 y^{2}-75+\frac{225}{y^{2}})=(5 y+\frac{15}{y})[(5 y)^{2}+(\frac{15}{y})^{2}-(5 y)(\frac{15}{y})]$

$=(5 y)^{3}+(\frac{15}{y})^{3}$

$=125 y^{3}+\frac{3375}{y^{3}}$

$=125(1)^{3}+\frac{3375}{(1)^{3}}$

$=125+3375$

$=3500$

Hence, $(5 y+\frac{15}{y})(25 y^{2}-75+\frac{225}{y^{2}})=3500$.    

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Simply Easy Learning

Updated on: 10-Oct-2022

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