Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Multiply $- 3 i (3 i)$ .

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Step 2.2.2.1

Multiply $3$ by $- 3$ .

$x^{2} - 9 i i$

Step 2.2.2.2

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

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

Step 2.2.2.3

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

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

Step 2.2.2.4

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

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

Step 2.2.2.5

Add $1$ and $1$ .

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

Step 2.2.3

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

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

Step 2.2.4

Multiply $- 9$ by $- 1$ .

$x^{2} + 9$