Algebra Examples

(3 - i) (3 + i)

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

Step 1

Expand

(3 - i) (3 + i)

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

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Step 1.1

Apply the distributive property.

3 (3 + i) - i (3 + i)

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

3 \cdot 3 + 3 i - i \cdot 3 - i i

$3 \cdot 3 + 3 i - i \cdot 3 - i i$

3 \cdot 3 + 3 i - i \cdot 3 - i i

$3 \cdot 3 + 3 i - i \cdot 3 - i i$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

3

$3$ by

3

$3$ .

9 + 3 i - i \cdot 3 - i i

$9 + 3 i - i \cdot 3 - i i$

Step 2.1.2

Multiply

3

$3$ by

- 1

$- 1$ .

9 + 3 i - 3 i - i i

$9 + 3 i - 3 i - i i$

Step 2.1.3

Multiply

- i i

$- i i$ .

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Step 2.1.3.1

Raise

i

$i$ to the power of

1

$1$ .

9 + 3 i - 3 i - (i^{1} i)

$9 + 3 i - 3 i - (i^{1} i)$

Step 2.1.3.2

Raise

i

$i$ to the power of

1

$1$ .

9 + 3 i - 3 i - (i^{1} i^{1})

$9 + 3 i - 3 i - (i^{1} i^{1})$

Step 2.1.3.3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

9 + 3 i - 3 i - i^{1 + 1}

$9 + 3 i - 3 i - i^{1 + 1}$

Step 2.1.3.4

Add

1

$1$ and

1

$1$ .

9 + 3 i - 3 i - i^{2}

$9 + 3 i - 3 i - i^{2}$

9 + 3 i - 3 i - i^{2}

$9 + 3 i - 3 i - i^{2}$

Step 2.1.4

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

9 + 3 i - 3 i - - 1

$9 + 3 i - 3 i - - 1$

Step 2.1.5

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

9 + 3 i - 3 i + 1

$9 + 3 i - 3 i + 1$

9 + 3 i - 3 i + 1

$9 + 3 i - 3 i + 1$

Step 2.2

Add

9

$9$ and

1

$1$ .

10 + 3 i - 3 i

$10 + 3 i - 3 i$

Step 2.3

Subtract

3 i

$3 i$ from

3 i

$3 i$ .

10 + 0

$10 + 0$

Step 2.4

Add

10

$10$ and

0

$0$ .

10

$10$

10

$10$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$