Question

Use the formula to find the factors.

(7) 729b³ − 64

Answer 1

729b³ − 64 can be factorised as:

$$\begin{gathered} 729b^3-64 \\ ={\left(9b\right)}^3-{\left(4\right)}^3 \\ =\left(9b-4\right)\left[{\left(9b\right)}^2+9b\times 4+{\left(4\right)}^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(9b-4\right)\left(81b^2+36b+16\right) \end{gathered}$$