Evaluate (x-5)^3

${(x - 5)}^{3}$

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot - 5 + 3 x {(- 5)}^{2} + {(- 5)}^{3}$

Simplify each term.

Multiply $- 5$ by $3$ .

$x^{3} - 15 x^{2} + 3 x {(- 5)}^{2} + {(- 5)}^{3}$

Raise $- 5$ to the power of $2$ .

$x^{3} - 15 x^{2} + 3 x \cdot 25 + {(- 5)}^{3}$

Multiply $25$ by $3$ .

$x^{3} - 15 x^{2} + 75 x + {(- 5)}^{3}$

Raise $- 5$ to the power of $3$ .

$x^{3} - 15 x^{2} + 75 x - 125$