Basic Math Examples

${(z - 7)}^{5}$

Step 1

Use the Binomial Theorem.

$z^{5} + 5 z^{4} \cdot - 7 + 10 z^{3} {(- 7)}^{2} + 10 z^{2} {(- 7)}^{3} + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2

Simplify each term.

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Step 2.1

Multiply $- 7$ by $5$ .

$z^{5} - 35 z^{4} + 10 z^{3} {(- 7)}^{2} + 10 z^{2} {(- 7)}^{3} + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2.2

Raise $- 7$ to the power of $2$ .

$z^{5} - 35 z^{4} + 10 z^{3} \cdot 49 + 10 z^{2} {(- 7)}^{3} + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2.3

Multiply $49$ by $10$ .

$z^{5} - 35 z^{4} + 490 z^{3} + 10 z^{2} {(- 7)}^{3} + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2.4

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

$z^{5} - 35 z^{4} + 490 z^{3} + 10 z^{2} \cdot - 343 + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2.5

Multiply $- 343$ by $10$ .

$z^{5} - 35 z^{4} + 490 z^{3} - 3430 z^{2} + 5 z {(- 7)}^{4} + {(- 7)}^{5}$

Step 2.6

Raise $- 7$ to the power of $4$ .

$z^{5} - 35 z^{4} + 490 z^{3} - 3430 z^{2} + 5 z \cdot 2401 + {(- 7)}^{5}$

Step 2.7

Multiply $2401$ by $5$ .

$z^{5} - 35 z^{4} + 490 z^{3} - 3430 z^{2} + 12005 z + {(- 7)}^{5}$

Step 2.8

Raise $- 7$ to the power of $5$ .

$z^{5} - 35 z^{4} + 490 z^{3} - 3430 z^{2} + 12005 z - 16807$