Algebra Examples

(2 + i) (3 - i)

$(2 + i) (3 - i)$

Step 1

Expand

(2 + i) (3 - i)

$(2 + i) (3 - i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 (3 - i) + i (3 - i)

$2 (3 - i) + i (3 - i)$

Step 1.2

Apply the distributive property.

2 \cdot 3 + 2 (- i) + i (3 - i)

$2 \cdot 3 + 2 (- i) + i (3 - i)$

Step 1.3

Apply the distributive property.

2 \cdot 3 + 2 (- i) + i \cdot 3 + i (- i)

$2 \cdot 3 + 2 (- i) + i \cdot 3 + i (- i)$

2 \cdot 3 + 2 (- i) + i \cdot 3 + i (- i)

$2 \cdot 3 + 2 (- i) + i \cdot 3 + i (- i)$

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

2

$2$ by

3

$3$ .

6 + 2 (- i) + i \cdot 3 + i (- i)

$6 + 2 (- i) + i \cdot 3 + i (- i)$

Step 2.1.2

Multiply

- 1

$- 1$ by

2

$2$ .

6 - 2 i + i \cdot 3 + i (- i)

$6 - 2 i + i \cdot 3 + i (- i)$

Step 2.1.3

Move

3

$3$ to the left of

i

$i$ .

6 - 2 i + 3 \cdot i + i (- i)

$6 - 2 i + 3 \cdot i + i (- i)$

Step 2.1.4

Multiply

i (- i)

$i (- i)$ .

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Step 2.1.4.1

Raise

i

$i$ to the power of

1

$1$ .

6 - 2 i + 3 i - (i^{1} i)

$6 - 2 i + 3 i - (i^{1} i)$

Step 2.1.4.2

Raise

i

$i$ to the power of

1

$1$ .

6 - 2 i + 3 i - (i^{1} i^{1})

$6 - 2 i + 3 i - (i^{1} i^{1})$

Step 2.1.4.3

Use the power rule

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

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

6 - 2 i + 3 i - i^{1 + 1}

$6 - 2 i + 3 i - i^{1 + 1}$

Step 2.1.4.4

Add

1

$1$ and

1

$1$ .

6 - 2 i + 3 i - i^{2}

$6 - 2 i + 3 i - i^{2}$

6 - 2 i + 3 i - i^{2}

$6 - 2 i + 3 i - i^{2}$

Step 2.1.5

Rewrite

i^{2}

$i^{2}$ as

- 1

$- 1$ .

6 - 2 i + 3 i - - 1

$6 - 2 i + 3 i - - 1$

Step 2.1.6

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

6 - 2 i + 3 i + 1

$6 - 2 i + 3 i + 1$

6 - 2 i + 3 i + 1

$6 - 2 i + 3 i + 1$

Step 2.2

Add

6

$6$ and

1

$1$ .

7 - 2 i + 3 i

$7 - 2 i + 3 i$

Step 2.3

Add

- 2 i

$- 2 i$ and

3 i

$3 i$ .

7 + i

$7 + i$

7 + i

$7 + i$

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

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