Evaluate (x-3)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $- 3$ by $3$ .

$x^{3} - 9 x^{2} + 3 x {(- 3)}^{2} + {(- 3)}^{3}$

Raise $- 3$ to the power of $2$ .

$x^{3} - 9 x^{2} + 3 x \cdot 9 + {(- 3)}^{3}$

Multiply $9$ by $3$ .

$x^{3} - 9 x^{2} + 27 x + {(- 3)}^{3}$

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

$x^{3} - 9 x^{2} + 27 x - 27$