Question

Use the formula to find the factors.

(3) 64a³ − 1

Answer 1

64a³ − 1 can be factorised as:

$$\begin{gathered} 64a^3-1 \\ ={\left(4a\right)}^2-{\left(1\right)}^3 \\ =\left(4a-1\right)\left[{\left(4a\right)}^2+4a\times 1+1^2\right]\left[\mathrm{using}\mathrm{the}\mathrm{formula}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\right] \\ =\left(4a-1\right)\left(16a^2+4a+1\right) \end{gathered}$$