Question
Factorize:
$x^3-12 x(x-4)-64$
$x^3-12 x(x-4)-64$
✓
Answer
$x^3-12 x(x-4)-64$
$=x^3-12 x^2+48 x-64$
$=(x)^3-3 \times x^2 \times 4+3 \times 4^2 \times x-4^3$
${\left[\because a^3-3 a^2 b+3 a b^2-b^3=(a-b)^3\right]}$
$=(x-4)(x-4)(x-4)$
$\therefore x^3-12 x(x-4)-64$
$=(x-4)(x-4)(x-4)$
$=x^3-12 x^2+48 x-64$
$=(x)^3-3 \times x^2 \times 4+3 \times 4^2 \times x-4^3$
${\left[\because a^3-3 a^2 b+3 a b^2-b^3=(a-b)^3\right]}$
$=(x-4)(x-4)(x-4)$
$\therefore x^3-12 x(x-4)-64$
$=(x-4)(x-4)(x-4)$
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