Factorise: a^3-12 a(a-4)-64 - Vidyadip

Question

Factorise:
$a^3-12 a(a-4)-64$

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Answer

$a^3-12 a(a-4)-64$
$a^3-12 a^2+48 a-64$
$=(a)^3-(4)^3-3(a)^2(4)+3(a)(4)^2$
$=(a-4)^3$
Hence, factorisation of $a^3-12 a(a-4)-64$ is $=(a-4)^3$

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