Question
Factorise: $a^3+\frac{8}{a^3}$
✓
Answer
$\begin{aligned} & \text { } a^3+\frac{8}{a^3} \\ & =a^3+\left(\frac{2}{a}\right)^3 \\ & \text { Here, } A=a \text { and } B=\frac{2}{a} \\ & \therefore \quad a^3+\frac{8}{a^3}=\left(a+\frac{2}{a}\right)\left[a^2-a\left(\frac{2}{a}\right)+\left(\frac{2}{a}\right)^2\right] \\ & \ldots\left[\because A^3+B^3=(A+B)\left(A^2-A B+B^2\right)\right] \\ & =\left(a+\frac{2}{a}\right)\left(a^2-2+\frac{4}{a^2}\right) \\ & \end{aligned}$
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