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

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Apply the product rule to $4 a$ .

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

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

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

Apply the product rule to $4 a$ .

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

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

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

Multiply $16$ by $3$ .

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

Multiply $- 4$ by $48$ .

$64 a^{3} - 192 a^{2} + 3 (4 a) {(- 4)}^{2} + {(- 4)}^{3}$

Multiply $4$ by $3$ .

$64 a^{3} - 192 a^{2} + 12 a {(- 4)}^{2} + {(- 4)}^{3}$

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

$64 a^{3} - 192 a^{2} + 12 a \cdot 16 + {(- 4)}^{3}$

Multiply $16$ by $12$ .

$64 a^{3} - 192 a^{2} + 192 a + {(- 4)}^{3}$

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

$64 a^{3} - 192 a^{2} + 192 a - 64$