Basic Math Examples

${(2 z - 4)}^{4}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 z$ .

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

Step 2.2

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

$16 z^{4} + 4 {(2 z)}^{3} \cdot - 4 + 6 {(2 z)}^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.3

Apply the product rule to $2 z$ .

$16 z^{4} + 4 (2^{3} z^{3}) \cdot - 4 + 6 {(2 z)}^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.4

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

$16 z^{4} + 4 (8 z^{3}) \cdot - 4 + 6 {(2 z)}^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.5

Multiply $8$ by $4$ .

$16 z^{4} + 32 z^{3} \cdot - 4 + 6 {(2 z)}^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.6

Multiply $- 4$ by $32$ .

$16 z^{4} - 128 z^{3} + 6 {(2 z)}^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.7

Apply the product rule to $2 z$ .

$16 z^{4} - 128 z^{3} + 6 (2^{2} z^{2}) {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.8

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

$16 z^{4} - 128 z^{3} + 6 (4 z^{2}) {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.9

Multiply $4$ by $6$ .

$16 z^{4} - 128 z^{3} + 24 z^{2} {(- 4)}^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.10

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

$16 z^{4} - 128 z^{3} + 24 z^{2} \cdot 16 + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.11

Multiply $16$ by $24$ .

$16 z^{4} - 128 z^{3} + 384 z^{2} + 4 (2 z) {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.12

Multiply $2$ by $4$ .

$16 z^{4} - 128 z^{3} + 384 z^{2} + 8 z {(- 4)}^{3} + {(- 4)}^{4}$

Step 2.13

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

$16 z^{4} - 128 z^{3} + 384 z^{2} + 8 z \cdot - 64 + {(- 4)}^{4}$

Step 2.14

Multiply $- 64$ by $8$ .

$16 z^{4} - 128 z^{3} + 384 z^{2} - 512 z + {(- 4)}^{4}$

Step 2.15

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

$16 z^{4} - 128 z^{3} + 384 z^{2} - 512 z + 256$