Algebra Examples

{(3 - i)}^{2}

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

Step 1

Rewrite

{(3 - i)}^{2}

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

(3 - i) (3 - i)

$(3 - i) (3 - i)$ .

(3 - i) (3 - i)

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

Step 2

Expand

(3 - i) (3 - i)

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

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Step 2.1

Apply the distributive property.

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

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

Step 2.2

Apply the distributive property.

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

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

Step 2.3

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 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

3

$3$ by

3

$3$ .

9 + 3 (- i) - i \cdot 3 - i (- i)

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

Step 3.1.2

Multiply

- 1

$- 1$ by

3

$3$ .

9 - 3 i - i \cdot 3 - i (- i)

$9 - 3 i - i \cdot 3 - i (- i)$

Step 3.1.3

Multiply

3

$3$ by

- 1

$- 1$ .

9 - 3 i - 3 i - i (- i)

$9 - 3 i - 3 i - i (- i)$

Step 3.1.4

Multiply

- i (- i)

$- i (- i)$ .

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Step 3.1.4.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

9 - 3 i - 3 i + 1 i i

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

Step 3.1.4.2

Raise

i

$i$ to the power of

1

$1$ .

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

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

Step 3.1.4.3

Raise

i

$i$ to the power of

1

$1$ .

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

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

Step 3.1.4.4

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 + 1 i^{1 + 1}

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

Step 3.1.4.5

Add

1

$1$ and

1

$1$ .

9 - 3 i - 3 i + 1 i^{2}

$9 - 3 i - 3 i + 1 i^{2}$

Step 3.1.4.6

Multiply

i^{2}

$i^{2}$ by

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 3.1.5

Rewrite

i^{2}

$i^{2}$ as

- 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 3.2

Subtract

1

$1$ from

9

$9$ .

8 - 3 i - 3 i

$8 - 3 i - 3 i$

Step 3.3

Subtract

3 i

$3 i$ from

- 3 i

$- 3 i$ .

8 - 6 i

$8 - 6 i$

8 - 6 i

$8 - 6 i$

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

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