Question

Factorise
a³ – 12a(a – 4) – 64

Answer 1

$$\begin{gathered} a^3-12a\left(a-4\right)-64=a^3-12a^2+48a-64 \\ ={\left(a\right)}^3-{\left(4\right)}^3-3{\left(a\right)}^2\left(4\right)+3\left(a\right){\left(4\right)}^2 \\ ={\left(a-4\right)}^3 \end{gathered}$$

Hence, factorisation of a³ – 12a(a – 4) – 64 is ${\left(a-4\right)}^3$.