Question

Factorise:

8p³ −\[\frac{27}{p^3}\]

Answer 1

It is known that,

a³ − b³ = (a − b)(a² + ab + b²)

\[\ 8p^3  - \frac{27}{p^3}\] 

\[ = \left(2p \right)^3 - \left(\frac{3}{p}\right)^3\] 

\[ = \left(2p - \frac{3}{p} \right)\left\{\left(2p \right)^2 + \left( \frac{3}{p} \right)^2 + \left(2p \right) \times \left(\frac{3}{p} \right) \right\}\] 

\[ = \left(2p - \frac{3}{p} \right)\left(4 p^2 + \frac{9}{p^2} + 6 \right)\]