Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Multiply $i (- i)$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.2.3

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

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

Step 2.2.2.4

Add $1$ and $1$ .

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

Step 2.2.3

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

$x^{2} - - 1$

Step 2.2.4

Multiply $- 1$ by $- 1$ .

$x^{2} + 1$