Algebra Examples

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

Step 1

Rewrite ${(i - 2)}^{2}$ as $(i - 2) (i - 2)$ .

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

Step 2

Expand $(i - 2) (i - 2)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

$(i i + i \cdot - 2 - 2 (i - 2)) (i + 2)$

Step 2.3

Apply the distributive property.

$(i i + i \cdot - 2 - 2 i - 2 \cdot - 2) (i + 2)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $i i$ .

Tap for more steps...

Step 3.1.1.1

Raise $i$ to the power of $1$ .

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

Step 3.1.1.2

Raise $i$ to the power of $1$ .

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

Step 3.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.1.1.4

Add $1$ and $1$ .

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

Step 3.1.2

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

$(- 1 + i \cdot - 2 - 2 i - 2 \cdot - 2) (i + 2)$

Step 3.1.3

Move $- 2$ to the left of $i$ .

$(- 1 - 2 \cdot i - 2 i - 2 \cdot - 2) (i + 2)$

Step 3.1.4

Multiply $- 2$ by $- 2$ .

$(- 1 - 2 i - 2 i + 4) (i + 2)$

Step 3.2

Add $- 1$ and $4$ .

$(3 - 2 i - 2 i) (i + 2)$

Step 3.3

Subtract $2 i$ from $- 2 i$ .

$(3 - 4 i) (i + 2)$

Step 4

Expand $(3 - 4 i) (i + 2)$ using the FOIL Method.

Tap for more steps...

Step 4.1

Apply the distributive property.

$3 (i + 2) - 4 i (i + 2)$

Step 4.2

Apply the distributive property.

$3 i + 3 \cdot 2 - 4 i (i + 2)$

Step 4.3

Apply the distributive property.

$3 i + 3 \cdot 2 - 4 i i - 4 i \cdot 2$

Step 5

Simplify and combine like terms.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Multiply $3$ by $2$ .

$3 i + 6 - 4 i i - 4 i \cdot 2$

Step 5.1.2

Multiply $- 4 i i$ .

Tap for more steps...

Step 5.1.2.1

Raise $i$ to the power of $1$ .

$3 i + 6 - 4 (i^{1} i) - 4 i \cdot 2$

Step 5.1.2.2

Raise $i$ to the power of $1$ .

$3 i + 6 - 4 (i^{1} i^{1}) - 4 i \cdot 2$

Step 5.1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 i + 6 - 4 i^{1 + 1} - 4 i \cdot 2$

Step 5.1.2.4

Add $1$ and $1$ .

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

Step 5.1.3

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

$3 i + 6 - 4 \cdot - 1 - 4 i \cdot 2$

Step 5.1.4

Multiply $- 4$ by $- 1$ .

$3 i + 6 + 4 - 4 i \cdot 2$

Step 5.1.5

Multiply $2$ by $- 4$ .

$3 i + 6 + 4 - 8 i$

Step 5.2

Subtract $8 i$ from $3 i$ .

$6 + 4 - 5 i$

Step 5.3

Add $6$ and $4$ .

$10 - 5 i$