Factorize : 8 p^3-27 p^3 - Vidyadip

Question

Factorize : $8 p^3-\frac{27}{p^3}$

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Answer

$\begin{aligned} & \text { } 8 p^3-\frac{27}{p^3} \\ & =(2 p)^3-\left(\frac{3}{p}\right)^3 \\ & \text { Here, } a=2 p \text { and } b=\frac{3}{p} \\ & \therefore \quad 8 p^3-\frac{27}{p^3}=\left(2 p-\frac{3}{p}\right)\left[(2 p)^2+(2 p)\left(\frac{3}{p}\right)+\left(\frac{3}{p}\right)^2\right] \\ & \ldots\left[\because a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right] \\ & =\left(2 p-\frac{3}{p}\right)\left(4 p^2+6+\frac{9}{p^2}\right) \\ & \end{aligned}$

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