Expand the Trigonometric Expression (b-2)^3

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $- 2$ by $3$ .

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

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

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

Multiply $4$ by $3$ .

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

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

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