Algebra Examples

${(6 y - 5)}^{4}$

Step 1

Use the Binomial Theorem.

${(6 y)}^{4} + 4 {(6 y)}^{3} \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $6 y$ .

$6^{4} y^{4} + 4 {(6 y)}^{3} \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.2

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

$1296 y^{4} + 4 {(6 y)}^{3} \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.3

Apply the product rule to $6 y$ .

$1296 y^{4} + 4 (6^{3} y^{3}) \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.4

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

$1296 y^{4} + 4 (216 y^{3}) \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.5

Multiply $216$ by $4$ .

$1296 y^{4} + 864 y^{3} \cdot - 5 + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.6

Multiply $- 5$ by $864$ .

$1296 y^{4} - 4320 y^{3} + 6 {(6 y)}^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.7

Apply the product rule to $6 y$ .

$1296 y^{4} - 4320 y^{3} + 6 (6^{2} y^{2}) {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.8

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

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Step 2.8.1

Move $6^{2}$ .

$1296 y^{4} - 4320 y^{3} + 6^{2} \cdot 6 y^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.8.2

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

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Step 2.8.2.1

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

$1296 y^{4} - 4320 y^{3} + 6^{2} \cdot 6^{1} y^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.8.2.2

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

$1296 y^{4} - 4320 y^{3} + 6^{2 + 1} y^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.8.3

Add $2$ and $1$ .

$1296 y^{4} - 4320 y^{3} + 6^{3} y^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.9

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

$1296 y^{4} - 4320 y^{3} + 216 y^{2} {(- 5)}^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.10

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

$1296 y^{4} - 4320 y^{3} + 216 y^{2} \cdot 25 + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.11

Multiply $25$ by $216$ .

$1296 y^{4} - 4320 y^{3} + 5400 y^{2} + 4 (6 y) {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.12

Multiply $6$ by $4$ .

$1296 y^{4} - 4320 y^{3} + 5400 y^{2} + 24 y {(- 5)}^{3} + {(- 5)}^{4}$

Step 2.13

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

$1296 y^{4} - 4320 y^{3} + 5400 y^{2} + 24 y \cdot - 125 + {(- 5)}^{4}$

Step 2.14

Multiply $- 125$ by $24$ .

$1296 y^{4} - 4320 y^{3} + 5400 y^{2} - 3000 y + {(- 5)}^{4}$

Step 2.15

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

$1296 y^{4} - 4320 y^{3} + 5400 y^{2} - 3000 y + 625$