Calculus Examples

${(z - 3)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Multiply $- 3$ by $3$ .

$z^{3} - 9 z^{2} + 3 z {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.2

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

$z^{3} - 9 z^{2} + 3 z \cdot 9 + {(- 3)}^{3}$

Step 2.3

Multiply $9$ by $3$ .

$z^{3} - 9 z^{2} + 27 z + {(- 3)}^{3}$

Step 2.4

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

$z^{3} - 9 z^{2} + 27 z - 27$