Expand the Trigonometric Expression (y-3)^7

${(y - 3)}^{7}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

Multiply $- 3$ by $7$ .

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

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

$y^{7} - 21 y^{6} + 21 y^{5} \cdot 9 + 35 y^{4} {(- 3)}^{3} + 35 y^{3} {(- 3)}^{4} + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Multiply $9$ by $21$ .

$y^{7} - 21 y^{6} + 189 y^{5} + 35 y^{4} {(- 3)}^{3} + 35 y^{3} {(- 3)}^{4} + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

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

$y^{7} - 21 y^{6} + 189 y^{5} + 35 y^{4} \cdot - 27 + 35 y^{3} {(- 3)}^{4} + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Multiply $- 27$ by $35$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 35 y^{3} {(- 3)}^{4} + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

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

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 35 y^{3} \cdot 81 + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Multiply $81$ by $35$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} + 21 y^{2} {(- 3)}^{5} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Raise $- 3$ to the power of $5$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} + 21 y^{2} \cdot - 243 + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Multiply $- 243$ by $21$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} - 5103 y^{2} + 7 y {(- 3)}^{6} + {(- 3)}^{7}$

Raise $- 3$ to the power of $6$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} - 5103 y^{2} + 7 y \cdot 729 + {(- 3)}^{7}$

Multiply $729$ by $7$ .

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} - 5103 y^{2} + 5103 y + {(- 3)}^{7}$

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

$y^{7} - 21 y^{6} + 189 y^{5} - 945 y^{4} + 2835 y^{3} - 5103 y^{2} + 5103 y - 2187$

Expand the Trigonometric Expression (y-3)^7

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