Evaluate (x-4)^3

${(x - 4)}^{3}$

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot - 4 + 3 x {(- 4)}^{2} + {(- 4)}^{3}$

Simplify each term.

Multiply $- 4$ by $3$ .

$x^{3} - 12 x^{2} + 3 x {(- 4)}^{2} + {(- 4)}^{3}$

Raise $- 4$ to the power of $2$ .

$x^{3} - 12 x^{2} + 3 x \cdot 16 + {(- 4)}^{3}$

Multiply $16$ by $3$ .

$x^{3} - 12 x^{2} + 48 x + {(- 4)}^{3}$

Raise $- 4$ to the power of $3$ .

$x^{3} - 12 x^{2} + 48 x - 64$