Expand the Trigonometric Expression (4y-3x)^4

${(4 y - 3 x)}^{4}$

Step 1

Use the Binomial Theorem.

${(4 y)}^{4} + 4 {(4 y)}^{3} (- 3 x) + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Step 2

Simplify each term.

Apply the product rule to $4 y$ .

$4^{4} y^{4} + 4 {(4 y)}^{3} (- 3 x) + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

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

$256 y^{4} + 4 {(4 y)}^{3} (- 3 x) + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Rewrite using the commutative property of multiplication.

$256 y^{4} + 4 \cdot - 3 {(4 y)}^{3} x + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Multiply $4$ by $- 3$ .

$256 y^{4} - 12 {(4 y)}^{3} x + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Apply the product rule to $4 y$ .

$256 y^{4} - 12 (4^{3} y^{3}) x + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

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

$256 y^{4} - 12 (64 y^{3}) x + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Multiply $64$ by $- 12$ .

$256 y^{4} - 768 y^{3} x + 6 {(4 y)}^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Apply the product rule to $4 y$ .

$256 y^{4} - 768 y^{3} x + 6 (4^{2} y^{2}) {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

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

$256 y^{4} - 768 y^{3} x + 6 (16 y^{2}) {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Multiply $16$ by $6$ .

$256 y^{4} - 768 y^{3} x + 96 y^{2} {(- 3 x)}^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Apply the product rule to $- 3 x$ .

$256 y^{4} - 768 y^{3} x + 96 y^{2} ({(- 3)}^{2} x^{2}) + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Rewrite using the commutative property of multiplication.

$256 y^{4} - 768 y^{3} x + 96 \cdot {(- 3)}^{2} y^{2} x^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

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

$256 y^{4} - 768 y^{3} x + 96 \cdot 9 y^{2} x^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Multiply $96$ by $9$ .

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} + 4 (4 y) {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Multiply $4$ by $4$ .

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} + 16 y {(- 3 x)}^{3} + {(- 3 x)}^{4}$

Apply the product rule to $- 3 x$ .

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} + 16 y ({(- 3)}^{3} x^{3}) + {(- 3 x)}^{4}$

Rewrite using the commutative property of multiplication.

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} + 16 \cdot {(- 3)}^{3} y x^{3} + {(- 3 x)}^{4}$

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

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} + 16 \cdot - 27 y x^{3} + {(- 3 x)}^{4}$

Multiply $16$ by $- 27$ .

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} - 432 y x^{3} + {(- 3 x)}^{4}$

Apply the product rule to $- 3 x$ .

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} - 432 y x^{3} + {(- 3)}^{4} x^{4}$

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

$256 y^{4} - 768 y^{3} x + 864 y^{2} x^{2} - 432 y x^{3} + 81 x^{4}$

Expand the Trigonometric Expression (4y-3x)^4

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