Expand the Trigonometric Expression (2-x)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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

$8 + 3 \cdot 2^{2} (- x) + 3 \cdot 2 {(- x)}^{2} + {(- x)}^{3}$

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

$8 + 3 \cdot 4 (- x) + 3 \cdot 2 {(- x)}^{2} + {(- x)}^{3}$

Multiply $3$ by $4$ .

$8 + 12 (- x) + 3 \cdot 2 {(- x)}^{2} + {(- x)}^{3}$

Multiply $- 1$ by $12$ .

$8 - 12 x + 3 \cdot 2 {(- x)}^{2} + {(- x)}^{3}$

Multiply $3$ by $2$ .

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

Apply the product rule to $- x$ .

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

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

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

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

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

Apply the product rule to $- x$ .

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

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

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