Simplify (3-6i)(3+6i)

$(3 - 6 i) (3 + 6 i)$

Step 1

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

Apply the distributive property.

$3 (3 + 6 i) - 6 i (3 + 6 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (6 i) - 6 i \cdot 3 - 6 i (6 i)$

Multiply $6$ by $3$ .

$9 + 18 i - 6 i \cdot 3 - 6 i (6 i)$

Multiply $3$ by $- 6$ .

$9 + 18 i - 18 i - 6 i (6 i)$

Multiply $- 6 i (6 i)$ .

Multiply $6$ by $- 6$ .

$9 + 18 i - 18 i - 36 i i$

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

$9 + 18 i - 18 i - 36 (i^{1} i)$

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

$9 + 18 i - 18 i - 36 (i^{1} i^{1})$

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

$9 + 18 i - 18 i - 36 i^{1 + 1}$

Add $1$ and $1$ .

$9 + 18 i - 18 i - 36 i^{2}$

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

$9 + 18 i - 18 i - 36 \cdot - 1$

Multiply $- 36$ by $- 1$ .

$9 + 18 i - 18 i + 36$

Add $9$ and $36$ .

$45 + 18 i - 18 i$

Subtract $18 i$ from $18 i$ .

$45 + 0$

Add $45$ and $0$ .

$45$