Question:
Factorise
$a^{3}-12 a(a-4)-64$
Solution:
$a^{3}-12 a(a-4)-64=a^{3}-12 a^{2}+48 a-64$
$=(a)^{3}-(4)^{3}-3(a)^{2}(4)+3(a)(4)^{2}$
$=(a-4)^{3}$
Hence, factorisation of $a^{3}-12 a(a-4)-64$ is $(a-4)^{3}$.
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