Question

Use the formula to find the factors.

(5) 216 − 27q³

Answer 1

216 − 27q³ can be factorised as:

$$\begin{gathered} 216-27q^3 \\ =27\left(8-q^3\right) \\ =27\left[{\left(2\right)}^3-{\left(q\right)}^3\right] \\ =27\left(2-q\right)\left(2^2+2\times q+q^2\right)\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =27\left(2-q\right)\left(4+2q+q^2\right) \end{gathered}$$