Simplify (x-2)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $- 2$ by $3$ .

$x^{3} - 6 x^{2} + 3 x {(- 2)}^{2} + {(- 2)}^{3}$

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

$x^{3} - 6 x^{2} + 3 x \cdot 4 + {(- 2)}^{3}$

Multiply $4$ by $3$ .

$x^{3} - 6 x^{2} + 12 x + {(- 2)}^{3}$

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

$x^{3} - 6 x^{2} + 12 x - 8$