Basic Math Examples

${(6 w - 3 y)}^{4}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $6 w$ .

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

Step 2.2

Raise $6$ to the power of $4$ .

$1296 w^{4} + 4 {(6 w)}^{3} (- 3 y) + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.3

Rewrite using the commutative property of multiplication.

$1296 w^{4} + 4 \cdot - 3 {(6 w)}^{3} y + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.4

Multiply $4$ by $- 3$ .

$1296 w^{4} - 12 {(6 w)}^{3} y + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.5

Apply the product rule to $6 w$ .

$1296 w^{4} - 12 (6^{3} w^{3}) y + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.6

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

$1296 w^{4} - 12 (216 w^{3}) y + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.7

Multiply $216$ by $- 12$ .

$1296 w^{4} - 2592 w^{3} y + 6 {(6 w)}^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.8

Apply the product rule to $6 w$ .

$1296 w^{4} - 2592 w^{3} y + 6 (6^{2} w^{2}) {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.9

Multiply $6$ by $6^{2}$ by adding the exponents.

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Step 2.9.1

Move $6^{2}$ .

$1296 w^{4} - 2592 w^{3} y + 6^{2} \cdot 6 w^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.9.2

Multiply $6^{2}$ by $6$ .

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Step 2.9.2.1

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

$1296 w^{4} - 2592 w^{3} y + 6^{2} \cdot 6^{1} w^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.9.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1296 w^{4} - 2592 w^{3} y + 6^{2 + 1} w^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.9.3

Add $2$ and $1$ .

$1296 w^{4} - 2592 w^{3} y + 6^{3} w^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.10

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

$1296 w^{4} - 2592 w^{3} y + 216 w^{2} {(- 3 y)}^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.11

Apply the product rule to $- 3 y$ .

$1296 w^{4} - 2592 w^{3} y + 216 w^{2} ({(- 3)}^{2} y^{2}) + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.12

Rewrite using the commutative property of multiplication.

$1296 w^{4} - 2592 w^{3} y + 216 \cdot {(- 3)}^{2} w^{2} y^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.13

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

$1296 w^{4} - 2592 w^{3} y + 216 \cdot 9 w^{2} y^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.14

Multiply $216$ by $9$ .

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} + 4 (6 w) {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.15

Multiply $6$ by $4$ .

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} + 24 w {(- 3 y)}^{3} + {(- 3 y)}^{4}$

Step 2.16

Apply the product rule to $- 3 y$ .

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} + 24 w ({(- 3)}^{3} y^{3}) + {(- 3 y)}^{4}$

Step 2.17

Rewrite using the commutative property of multiplication.

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} + 24 \cdot {(- 3)}^{3} w y^{3} + {(- 3 y)}^{4}$

Step 2.18

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

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} + 24 \cdot - 27 w y^{3} + {(- 3 y)}^{4}$

Step 2.19

Multiply $24$ by $- 27$ .

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} - 648 w y^{3} + {(- 3 y)}^{4}$

Step 2.20

Apply the product rule to $- 3 y$ .

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} - 648 w y^{3} + {(- 3)}^{4} y^{4}$

Step 2.21

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

$1296 w^{4} - 2592 w^{3} y + 1944 w^{2} y^{2} - 648 w y^{3} + 81 y^{4}$