Simplify (x+3i)(x-3i)

$(x + 3 i) (x - 3 i)$

Step 1

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

Apply the distributive property.

$x (x - 3 i) + 3 i (x - 3 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- 3 i) + 3 i x + 3 i (- 3 i)$ .

Reorder the factors in the terms $x (- 3 i)$ and $3 i x$ .

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

Add $- 3 i x$ and $3 i x$ .

$x \cdot x + 0 + 3 i (- 3 i)$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $3 i (- 3 i)$ .

Multiply $- 3$ by $3$ .

$x^{2} - 9 i i$

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

$x^{2} - 9 (i^{1} i)$

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

$x^{2} - 9 (i^{1} i^{1})$

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

$x^{2} - 9 i^{1 + 1}$

Add $1$ and $1$ .

$x^{2} - 9 i^{2}$

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

$x^{2} - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$x^{2} + 9$