Expand the Trigonometric Expression (4a-6)^3

${(4 a - 6)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Apply the product rule to $4 a$ .

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

Raise $4$ to the power of $3$ .

$64 a^{3} + 3 {(4 a)}^{2} \cdot - 6 + 3 (4 a) {(- 6)}^{2} + {(- 6)}^{3}$

Apply the product rule to $4 a$ .

$64 a^{3} + 3 (4^{2} a^{2}) \cdot - 6 + 3 (4 a) {(- 6)}^{2} + {(- 6)}^{3}$

Raise $4$ to the power of $2$ .

$64 a^{3} + 3 (16 a^{2}) \cdot - 6 + 3 (4 a) {(- 6)}^{2} + {(- 6)}^{3}$

Multiply $16$ by $3$ .

$64 a^{3} + 48 a^{2} \cdot - 6 + 3 (4 a) {(- 6)}^{2} + {(- 6)}^{3}$

Multiply $- 6$ by $48$ .

$64 a^{3} - 288 a^{2} + 3 (4 a) {(- 6)}^{2} + {(- 6)}^{3}$

Multiply $4$ by $3$ .

$64 a^{3} - 288 a^{2} + 12 a {(- 6)}^{2} + {(- 6)}^{3}$

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

$64 a^{3} - 288 a^{2} + 12 a \cdot 36 + {(- 6)}^{3}$

Multiply $36$ by $12$ .

$64 a^{3} - 288 a^{2} + 432 a + {(- 6)}^{3}$

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

$64 a^{3} - 288 a^{2} + 432 a - 216$