Basic Math Examples

$(2 - 6 i) (3 - 3 i)$

Step 1

Expand $(2 - 6 i) (3 - 3 i)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$2 (3 - 3 i) - 6 i (3 - 3 i)$

Step 1.2

Apply the distributive property.

$2 \cdot 3 + 2 (- 3 i) - 6 i (3 - 3 i)$

Step 1.3

Apply the distributive property.

$2 \cdot 3 + 2 (- 3 i) - 6 i \cdot 3 - 6 i (- 3 i)$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $2$ by $3$ .

$6 + 2 (- 3 i) - 6 i \cdot 3 - 6 i (- 3 i)$

Step 2.1.2

Multiply $- 3$ by $2$ .

$6 - 6 i - 6 i \cdot 3 - 6 i (- 3 i)$

Step 2.1.3

Multiply $3$ by $- 6$ .

$6 - 6 i - 18 i - 6 i (- 3 i)$

Step 2.1.4

Multiply $- 6 i (- 3 i)$ .

Tap for more steps...

Step 2.1.4.1

Multiply $- 3$ by $- 6$ .

$6 - 6 i - 18 i + 18 i i$

Step 2.1.4.2

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

$6 - 6 i - 18 i + 18 (i^{1} i)$

Step 2.1.4.3

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

$6 - 6 i - 18 i + 18 (i^{1} i^{1})$

Step 2.1.4.4

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

$6 - 6 i - 18 i + 18 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$6 - 6 i - 18 i + 18 i^{2}$

Step 2.1.5

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

$6 - 6 i - 18 i + 18 \cdot - 1$

Step 2.1.6

Multiply $18$ by $- 1$ .

$6 - 6 i - 18 i - 18$

Step 2.2

Subtract $18$ from $6$ .

$- 12 - 6 i - 18 i$

Step 2.3

Subtract $18 i$ from $- 6 i$ .

$- 12 - 24 i$