Expand the Trigonometric Expression (6a-1)^3

${(6 a - 1)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Apply the product rule to $6 a$ .

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

Raise $6$ to the power of $3$ .

$216 a^{3} + 3 {(6 a)}^{2} \cdot - 1 + 3 (6 a) {(- 1)}^{2} + {(- 1)}^{3}$

Apply the product rule to $6 a$ .

$216 a^{3} + 3 (6^{2} a^{2}) \cdot - 1 + 3 (6 a) {(- 1)}^{2} + {(- 1)}^{3}$

Raise $6$ to the power of $2$ .

$216 a^{3} + 3 (36 a^{2}) \cdot - 1 + 3 (6 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $36$ by $3$ .

$216 a^{3} + 108 a^{2} \cdot - 1 + 3 (6 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $- 1$ by $108$ .

$216 a^{3} - 108 a^{2} + 3 (6 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $6$ by $3$ .

$216 a^{3} - 108 a^{2} + 18 a {(- 1)}^{2} + {(- 1)}^{3}$

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

$216 a^{3} - 108 a^{2} + 18 a \cdot 1 + {(- 1)}^{3}$

Multiply $18$ by $1$ .

$216 a^{3} - 108 a^{2} + 18 a + {(- 1)}^{3}$

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

$216 a^{3} - 108 a^{2} + 18 a - 1$