Expand the Trigonometric Expression (4t-3)^5

${(4 t - 3)}^{5}$

Step 1

Use the Binomial Theorem.

${(4 t)}^{5} + 5 {(4 t)}^{4} \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2

Simplify each term.

Apply the product rule to $4 t$ .

$4^{5} t^{5} + 5 {(4 t)}^{4} \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Raise $4$ to the power of $5$ .

$1024 t^{5} + 5 {(4 t)}^{4} \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Apply the product rule to $4 t$ .

$1024 t^{5} + 5 (4^{4} t^{4}) \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} + 5 (256 t^{4}) \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $256$ by $5$ .

$1024 t^{5} + 1280 t^{4} \cdot - 3 + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $- 3$ by $1280$ .

$1024 t^{5} - 3840 t^{4} + 10 {(4 t)}^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Apply the product rule to $4 t$ .

$1024 t^{5} - 3840 t^{4} + 10 (4^{3} t^{3}) {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} - 3840 t^{4} + 10 (64 t^{3}) {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $64$ by $10$ .

$1024 t^{5} - 3840 t^{4} + 640 t^{3} {(- 3)}^{2} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} - 3840 t^{4} + 640 t^{3} \cdot 9 + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $9$ by $640$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} + 10 {(4 t)}^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Apply the product rule to $4 t$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} + 10 (4^{2} t^{2}) {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} + 10 (16 t^{2}) {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $16$ by $10$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} + 160 t^{2} {(- 3)}^{3} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} + 160 t^{2} \cdot - 27 + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $- 27$ by $160$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} - 4320 t^{2} + 5 (4 t) {(- 3)}^{4} + {(- 3)}^{5}$

Multiply $4$ by $5$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} - 4320 t^{2} + 20 t {(- 3)}^{4} + {(- 3)}^{5}$

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

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} - 4320 t^{2} + 20 t \cdot 81 + {(- 3)}^{5}$

Multiply $81$ by $20$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} - 4320 t^{2} + 1620 t + {(- 3)}^{5}$

Raise $- 3$ to the power of $5$ .

$1024 t^{5} - 3840 t^{4} + 5760 t^{3} - 4320 t^{2} + 1620 t - 243$

Expand the Trigonometric Expression (4t-3)^5

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