Algebra Examples

$(2 \sqrt{- 3} - 4) (3 \sqrt{- 2} + 3)$

Step 1

Rewrite $- 3$ as $- 1 (3)$ .

$(2 \sqrt{- 1 (3)} - 4) (3 \sqrt{- 2} + 3)$

Step 2

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$(2 (\sqrt{- 1} \cdot \sqrt{3}) - 4) (3 \sqrt{- 2} + 3)$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

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

Step 4

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 5

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

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

Step 6

Rewrite $\sqrt{- 1}$ as $i$ .

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

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Remove parentheses.

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

Step 7.2

Remove parentheses.

$(2 i \sqrt{3} - 4) (3 i \sqrt{2} + 3)$

Step 8

Expand $(2 i \sqrt{3} - 4) (3 i \sqrt{2} + 3)$ using the FOIL Method.

Tap for more steps...

Step 8.1

Apply the distributive property.

$2 i \sqrt{3} (3 i \sqrt{2} + 3) - 4 (3 i \sqrt{2} + 3)$

Step 8.2

Apply the distributive property.

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

Step 8.3

Apply the distributive property.

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

Step 9

Simplify terms.

Tap for more steps...

Step 9.1

Simplify each term.

Tap for more steps...

Step 9.1.1

Multiply $2 i \sqrt{3} (3 i \sqrt{2})$ .

Tap for more steps...

Step 9.1.1.1

Multiply $3$ by $2$ .

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

Step 9.1.1.2

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

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

Step 9.1.1.3

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

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

Step 9.1.1.4

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

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

Step 9.1.1.5

Add $1$ and $1$ .

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

Step 9.1.1.6

Combine using the product rule for radicals.

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

Step 9.1.1.7

Multiply $2$ by $3$ .

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

Step 9.1.2

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

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

Step 9.1.3

Multiply $6$ by $- 1$ .

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

Step 9.1.4

Multiply $3$ by $2$ .

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

Step 9.1.5

Multiply $3$ by $- 4$ .

$- 6 \sqrt{6} + 6 i \sqrt{3} - 12 (i \sqrt{2}) - 4 \cdot 3$

Step 9.1.6

Multiply $- 4$ by $3$ .

$- 6 \sqrt{6} + 6 i \sqrt{3} - 12 i \sqrt{2} - 12$

Step 9.2

Reorder $- 6 \sqrt{6} + 6 i \sqrt{3} - 12 i \sqrt{2}$ and $- 12$ .

$- 12 - 6 \sqrt{6} + 6 i \sqrt{3} - 12 i \sqrt{2}$