Trigonometry Examples

${(2 x - 3)}^{5}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the product rule to $2 x$ .

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

Step 2.2

Raise $2$ to the power of $5$ .

$32 x^{5} + 5 {(2 x)}^{4} \cdot - 3 + 10 {(2 x)}^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.3

Apply the product rule to $2 x$ .

$32 x^{5} + 5 (2^{4} x^{4}) \cdot - 3 + 10 {(2 x)}^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.4

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

$32 x^{5} + 5 (16 x^{4}) \cdot - 3 + 10 {(2 x)}^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.5

Multiply $16$ by $5$ .

$32 x^{5} + 80 x^{4} \cdot - 3 + 10 {(2 x)}^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.6

Multiply $- 3$ by $80$ .

$32 x^{5} - 240 x^{4} + 10 {(2 x)}^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.7

Apply the product rule to $2 x$ .

$32 x^{5} - 240 x^{4} + 10 (2^{3} x^{3}) {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.8

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

$32 x^{5} - 240 x^{4} + 10 (8 x^{3}) {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.9

Multiply $8$ by $10$ .

$32 x^{5} - 240 x^{4} + 80 x^{3} {(- 3)}^{2} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.10

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

$32 x^{5} - 240 x^{4} + 80 x^{3} \cdot 9 + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.11

Multiply $9$ by $80$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} + 10 {(2 x)}^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.12

Apply the product rule to $2 x$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} + 10 (2^{2} x^{2}) {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.13

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

$32 x^{5} - 240 x^{4} + 720 x^{3} + 10 (4 x^{2}) {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.14

Multiply $4$ by $10$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} + 40 x^{2} {(- 3)}^{3} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.15

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

$32 x^{5} - 240 x^{4} + 720 x^{3} + 40 x^{2} \cdot - 27 + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.16

Multiply $- 27$ by $40$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 5 (2 x) {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.17

Multiply $2$ by $5$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 10 x {(- 3)}^{4} + {(- 3)}^{5}$

Step 2.18

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

$32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 10 x \cdot 81 + {(- 3)}^{5}$

Step 2.19

Multiply $81$ by $10$ .

$32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 810 x + {(- 3)}^{5}$

Step 2.20

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

$32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 810 x - 243$