Factorize:$x^3 - 12x(x - 4) - 64$

Given:

$x^3 - 12x(x - 4) - 64$

To do:

We have to factorize the given expression.

Solution:

We know that,

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

$(a - b)^3 = a^3 - b^3 - 3ab(a - b)$

Therefore,

$x^3 - 12x(x - 4) - 64 = x^3 - 12x^2 + 48x - 64$

$= (x)^3 - 3 \times x^2 \times 4 + 3 \times x \times (4)^2 - (4)^3$

$= (x - 4)^3$

$= (x - 4) (x - 4) (x - 4)$

Hence, $x^3 - 12x(x - 4) - 64 = (x - 4) (x - 4) (x - 4)$.