Pre-Algebra Examples

${(3 x - 1)}^{7}$

Step 1

Use the Binomial Theorem.

${(3 x)}^{7} + 7 {(3 x)}^{6} \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the product rule to $3 x$ .

$3^{7} x^{7} + 7 {(3 x)}^{6} \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.2

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

$2187 x^{7} + 7 {(3 x)}^{6} \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.3

Apply the product rule to $3 x$ .

$2187 x^{7} + 7 (3^{6} x^{6}) \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.4

Raise $3$ to the power of $6$ .

$2187 x^{7} + 7 (729 x^{6}) \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.5

Multiply $729$ by $7$ .

$2187 x^{7} + 5103 x^{6} \cdot - 1 + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.6

Multiply $- 1$ by $5103$ .

$2187 x^{7} - 5103 x^{6} + 21 {(3 x)}^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.7

Apply the product rule to $3 x$ .

$2187 x^{7} - 5103 x^{6} + 21 (3^{5} x^{5}) {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.8

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

$2187 x^{7} - 5103 x^{6} + 21 (243 x^{5}) {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.9

Multiply $243$ by $21$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} {(- 1)}^{2} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.10

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

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} \cdot 1 + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.11

Multiply $5103$ by $1$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} + 35 {(3 x)}^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.12

Apply the product rule to $3 x$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} + 35 (3^{4} x^{4}) {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.13

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

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} + 35 (81 x^{4}) {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.14

Multiply $81$ by $35$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} + 2835 x^{4} {(- 1)}^{3} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.15

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

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} + 2835 x^{4} \cdot - 1 + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.16

Multiply $- 1$ by $2835$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 35 {(3 x)}^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.17

Apply the product rule to $3 x$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 35 (3^{3} x^{3}) {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.18

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

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 35 (27 x^{3}) {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.19

Multiply $27$ by $35$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} {(- 1)}^{4} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.20

Raise $- 1$ to the power of $4$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} \cdot 1 + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.21

Multiply $945$ by $1$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} + 21 {(3 x)}^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.22

Apply the product rule to $3 x$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} + 21 (3^{2} x^{2}) {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.23

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

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} + 21 (9 x^{2}) {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.24

Multiply $9$ by $21$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} + 189 x^{2} {(- 1)}^{5} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.25

Raise $- 1$ to the power of $5$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} + 189 x^{2} \cdot - 1 + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.26

Multiply $- 1$ by $189$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} - 189 x^{2} + 7 (3 x) {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.27

Multiply $3$ by $7$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} - 189 x^{2} + 21 x {(- 1)}^{6} + {(- 1)}^{7}$

Step 2.28

Raise $- 1$ to the power of $6$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} - 189 x^{2} + 21 x \cdot 1 + {(- 1)}^{7}$

Step 2.29

Multiply $21$ by $1$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} - 189 x^{2} + 21 x + {(- 1)}^{7}$

Step 2.30

Raise $- 1$ to the power of $7$ .

$2187 x^{7} - 5103 x^{6} + 5103 x^{5} - 2835 x^{4} + 945 x^{3} - 189 x^{2} + 21 x - 1$