Algebra Examples

${(i - 2)}^{3} - (i - 2)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Factor out $i^{2}$ .

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

Step 1.2.2

Rewrite $i^{2}$ as $- 1$ .

$- 1 \cdot i + 3 i^{2} \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Step 1.2.3

Rewrite $- 1 i$ as $- i$ .

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

Step 1.2.4

Rewrite $i^{2}$ as $- 1$ .

$- i + 3 \cdot - 1 \cdot - 2 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Step 1.2.5

Multiply $3 \cdot - 1 \cdot - 2$ .

Tap for more steps...

Step 1.2.5.1

Multiply $3$ by $- 1$ .

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

Step 1.2.5.2

Multiply $- 3$ by $- 2$ .

$- i + 6 + 3 i {(- 2)}^{2} + {(- 2)}^{3} - (i - 2)$

Step 1.2.6

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

$- i + 6 + 3 i \cdot 4 + {(- 2)}^{3} - (i - 2)$

Step 1.2.7

Multiply $4$ by $3$ .

$- i + 6 + 12 i + {(- 2)}^{3} - (i - 2)$

Step 1.2.8

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

$- i + 6 + 12 i - 8 - (i - 2)$

Step 1.3

Add $- i$ and $12 i$ .

$6 + 11 i - 8 - (i - 2)$

Step 1.4

Subtract $8$ from $6$ .

$- 2 + 11 i - (i - 2)$

Step 1.5

Apply the distributive property.

$- 2 + 11 i - i - - 2$

Step 1.6

Multiply $- 1$ by $- 2$ .

$- 2 + 11 i - i + 2$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $- 2$ and $2$ .

$0 + 11 i - i$

Step 2.2

Add $0$ and $11 i$ .

$11 i - i$

Step 2.3

Subtract $i$ from $11 i$ .

$10 i$