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 $- 3 i x$ .

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

Subtract $3 i x$ from $3 i x$ .

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

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 $- 1$ .

$x^{2} + 9$