Find the cube of : (3 a-1 a )(a 0) - Vidyadip

Question

Find the cube of$ : \left(3 a-\frac{1}{a}\right)(a \neq 0)$

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Answer

$ (a-b)^3=a^3-3 a^2 b+3 a b^2-b^3$
$ \left(3 a-\frac{1}{a}\right)^3$
$ =(3 a)^3-3 \times(3 a)^2 \times \frac{1}{a}+3 \cdot 3 a\left(\frac{1}{a}\right)^2-\left(\frac{1}{a}\right)^3$
$ =27 a^3-3 \cdot 9 a^2 \cdot \frac{1}{a}+9 a \cdot \frac{1}{a^2}-\frac{1}{a^3}$
$ =27 a^3-27 a+\frac{9}{a}-\frac{1}{a^3} .$

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