Basic Math Examples

${(3 y - 11)}^{4}$

Step 1

Use the Binomial Theorem.

${(3 y)}^{4} + 4 {(3 y)}^{3} \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $3 y$ .

$3^{4} y^{4} + 4 {(3 y)}^{3} \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.2

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

$81 y^{4} + 4 {(3 y)}^{3} \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.3

Apply the product rule to $3 y$ .

$81 y^{4} + 4 (3^{3} y^{3}) \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.4

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

$81 y^{4} + 4 (27 y^{3}) \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.5

Multiply $27$ by $4$ .

$81 y^{4} + 108 y^{3} \cdot - 11 + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.6

Multiply $- 11$ by $108$ .

$81 y^{4} - 1188 y^{3} + 6 {(3 y)}^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.7

Apply the product rule to $3 y$ .

$81 y^{4} - 1188 y^{3} + 6 (3^{2} y^{2}) {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.8

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

$81 y^{4} - 1188 y^{3} + 6 (9 y^{2}) {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.9

Multiply $9$ by $6$ .

$81 y^{4} - 1188 y^{3} + 54 y^{2} {(- 11)}^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.10

Raise $- 11$ to the power of $2$ .

$81 y^{4} - 1188 y^{3} + 54 y^{2} \cdot 121 + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.11

Multiply $121$ by $54$ .

$81 y^{4} - 1188 y^{3} + 6534 y^{2} + 4 (3 y) {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.12

Multiply $3$ by $4$ .

$81 y^{4} - 1188 y^{3} + 6534 y^{2} + 12 y {(- 11)}^{3} + {(- 11)}^{4}$

Step 2.13

Raise $- 11$ to the power of $3$ .

$81 y^{4} - 1188 y^{3} + 6534 y^{2} + 12 y \cdot - 1331 + {(- 11)}^{4}$

Step 2.14

Multiply $- 1331$ by $12$ .

$81 y^{4} - 1188 y^{3} + 6534 y^{2} - 15972 y + {(- 11)}^{4}$

Step 2.15

Raise $- 11$ to the power of $4$ .

$81 y^{4} - 1188 y^{3} + 6534 y^{2} - 15972 y + 14641$