Expand the Trigonometric Expression (7k-w)^3

${(7 k - w)}^{3}$

Step 1

Use the Binomial Theorem.

${(7 k)}^{3} + 3 {(7 k)}^{2} (- w) + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Step 2

Simplify each term.

Apply the product rule to $7 k$ .

$7^{3} k^{3} + 3 {(7 k)}^{2} (- w) + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Raise $7$ to the power of $3$ .

$343 k^{3} + 3 {(7 k)}^{2} (- w) + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Rewrite using the commutative property of multiplication.

$343 k^{3} + 3 \cdot - 1 {(7 k)}^{2} w + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Multiply $3$ by $- 1$ .

$343 k^{3} - 3 {(7 k)}^{2} w + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Apply the product rule to $7 k$ .

$343 k^{3} - 3 (7^{2} k^{2}) w + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Raise $7$ to the power of $2$ .

$343 k^{3} - 3 (49 k^{2}) w + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Multiply $49$ by $- 3$ .

$343 k^{3} - 147 k^{2} w + 3 (7 k) {(- w)}^{2} + {(- w)}^{3}$

Multiply $7$ by $3$ .

$343 k^{3} - 147 k^{2} w + 21 k {(- w)}^{2} + {(- w)}^{3}$

Apply the product rule to $- w$ .

$343 k^{3} - 147 k^{2} w + 21 k ({(- 1)}^{2} w^{2}) + {(- w)}^{3}$

Rewrite using the commutative property of multiplication.

$343 k^{3} - 147 k^{2} w + 21 \cdot {(- 1)}^{2} k w^{2} + {(- w)}^{3}$

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

$343 k^{3} - 147 k^{2} w + 21 \cdot 1 k w^{2} + {(- w)}^{3}$

Multiply $21$ by $1$ .

$343 k^{3} - 147 k^{2} w + 21 k w^{2} + {(- w)}^{3}$

Apply the product rule to $- w$ .

$343 k^{3} - 147 k^{2} w + 21 k w^{2} + {(- 1)}^{3} w^{3}$

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

$343 k^{3} - 147 k^{2} w + 21 k w^{2} - w^{3}$