Basic Math Examples

${(d - 3)}^{6}$

Step 1

Use the Binomial Theorem.

$d^{6} + 6 d^{5} \cdot - 3 + 15 d^{4} {(- 3)}^{2} + 20 d^{3} {(- 3)}^{3} + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2

Simplify each term.

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Step 2.1

Multiply $- 3$ by $6$ .

$d^{6} - 18 d^{5} + 15 d^{4} {(- 3)}^{2} + 20 d^{3} {(- 3)}^{3} + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.2

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

$d^{6} - 18 d^{5} + 15 d^{4} \cdot 9 + 20 d^{3} {(- 3)}^{3} + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.3

Multiply $9$ by $15$ .

$d^{6} - 18 d^{5} + 135 d^{4} + 20 d^{3} {(- 3)}^{3} + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.4

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

$d^{6} - 18 d^{5} + 135 d^{4} + 20 d^{3} \cdot - 27 + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.5

Multiply $- 27$ by $20$ .

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 15 d^{2} {(- 3)}^{4} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.6

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

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 15 d^{2} \cdot 81 + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.7

Multiply $81$ by $15$ .

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 1215 d^{2} + 6 d {(- 3)}^{5} + {(- 3)}^{6}$

Step 2.8

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

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 1215 d^{2} + 6 d \cdot - 243 + {(- 3)}^{6}$

Step 2.9

Multiply $- 243$ by $6$ .

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 1215 d^{2} - 1458 d + {(- 3)}^{6}$

Step 2.10

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

$d^{6} - 18 d^{5} + 135 d^{4} - 540 d^{3} + 1215 d^{2} - 1458 d + 729$