Expand the Trigonometric Expression (z-1)^7

${(z - 1)}^{7}$

Step 1

Use the Binomial Theorem.

$z^{7} + 7 z^{6} \cdot - 1 + 21 z^{5} {(- 1)}^{2} + 35 z^{4} {(- 1)}^{3} + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Step 2

Simplify each term.

Multiply $- 1$ by $7$ .

$z^{7} - 7 z^{6} + 21 z^{5} {(- 1)}^{2} + 35 z^{4} {(- 1)}^{3} + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Raise $- 1$ to the power of $2$ .

$z^{7} - 7 z^{6} + 21 z^{5} \cdot 1 + 35 z^{4} {(- 1)}^{3} + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Multiply $21$ by $1$ .

$z^{7} - 7 z^{6} + 21 z^{5} + 35 z^{4} {(- 1)}^{3} + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Raise $- 1$ to the power of $3$ .

$z^{7} - 7 z^{6} + 21 z^{5} + 35 z^{4} \cdot - 1 + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Multiply $- 1$ by $35$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} {(- 1)}^{4} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Raise $- 1$ to the power of $4$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} \cdot 1 + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Multiply $35$ by $1$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} + 21 z^{2} {(- 1)}^{5} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Raise $- 1$ to the power of $5$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} + 21 z^{2} \cdot - 1 + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

Multiply $- 1$ by $21$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} - 21 z^{2} + 7 z {(- 1)}^{6} + {(- 1)}^{7}$

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

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} - 21 z^{2} + 7 z \cdot 1 + {(- 1)}^{7}$

Multiply $7$ by $1$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} - 21 z^{2} + 7 z + {(- 1)}^{7}$

Raise $- 1$ to the power of $7$ .

$z^{7} - 7 z^{6} + 21 z^{5} - 35 z^{4} + 35 z^{3} - 21 z^{2} + 7 z - 1$

Expand the Trigonometric Expression (z-1)^7

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