Question

Use the formula to find the factors.

(2) 125m³ − 27n³

Answer 1

125m³ − 27n³ can be factorised as:

$$\begin{gathered} 125m^3-27n^3 \\ ={\left(5m\right)}^3-{\left(3n\right)}^3 \\ =\left(5m-3n\right)\left[{\left(5n\right)}^2+5m\times 3n+{\left(3n\right)}^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(5m-3n\right)\left(25n^2+15mn+9n^2\right) \end{gathered}$$