Simplify ((x-1)^3-1)^3

${({(x - 1)}^{3} - 1)}^{3}$

Simplify each term.

Use the Binomial Theorem.

${(x^{3} + 3 x^{2} \cdot - 1 + 3 x {(- 1)}^{2} + {(- 1)}^{3} - 1)}^{3}$

Simplify each term.

Multiply $- 1$ by $3$ .

${(x^{3} - 3 x^{2} + 3 x {(- 1)}^{2} + {(- 1)}^{3} - 1)}^{3}$

Raise $- 1$ to the power of $2$ .

${(x^{3} - 3 x^{2} + 3 x \cdot 1 + {(- 1)}^{3} - 1)}^{3}$

Multiply $3$ by $1$ .

${(x^{3} - 3 x^{2} + 3 x + {(- 1)}^{3} - 1)}^{3}$

Raise $- 1$ to the power of $3$ .

${(x^{3} - 3 x^{2} + 3 x - 1 - 1)}^{3}$

Subtract $1$ from $- 1$ .

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