Evaluate (1-x)^3

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

Use the Binomial Theorem.

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

Simplify each term.

One to any power is one.

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

One to any power is one.

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

Multiply $3$ by $1$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $3$ by $1$ .

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

Apply the product rule to $- x$ .

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

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

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

Multiply $x^{2}$ by $1$ .

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

Apply the product rule to $- x$ .

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

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

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