Evaluate (1-2x)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

One to any power is one.

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

One to any power is one.

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

Multiply $3$ by $1$ .

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

Multiply $- 2$ by $3$ .

$1 - 6 x + 3 \cdot 1 {(- 2 x)}^{2} + {(- 2 x)}^{3}$

Multiply $3$ by $1$ .

$1 - 6 x + 3 {(- 2 x)}^{2} + {(- 2 x)}^{3}$

Apply the product rule to $- 2 x$ .

$1 - 6 x + 3 ({(- 2)}^{2} x^{2}) + {(- 2 x)}^{3}$

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

$1 - 6 x + 3 (4 x^{2}) + {(- 2 x)}^{3}$

Multiply $4$ by $3$ .

$1 - 6 x + 12 x^{2} + {(- 2 x)}^{3}$

Apply the product rule to $- 2 x$ .

$1 - 6 x + 12 x^{2} + {(- 2)}^{3} x^{3}$

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

$1 - 6 x + 12 x^{2} - 8 x^{3}$