Question

Use the formula to find the factors.

(9) $8y^3-{\frac{27}{y}}^3$

Answer 1

$8y^3-{\frac{27}{y}}^3$ can be factorised as:
$$\begin{gathered} 8y^3-\frac{27}{y^3} \\ ={\left(2y\right)}^3-{\left(\frac{3}{y}\right)}^3 \\ =\left(2y-\frac{3}{y}\right)\left[{\left(2y\right)}^2+2y\times \frac{3}{y}+{\left(\frac{3}{y}\right)}^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(2y-\frac{3}{y}\right)\left(4y^2+6+\frac{9}{y^2}\right) \end{gathered}$$