Algebra Examples

(2 + i) (2 - i)

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

Step 1

Expand

(2 + i) (2 - i)

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

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Step 1.1

Apply the distributive property.

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

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

Step 1.2

Apply the distributive property.

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

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

Step 1.3

Apply the distributive property.

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

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

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

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

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

2

$2$ .

4 + 2 (- i) + i \cdot 2 + i (- i)

$4 + 2 (- i) + i \cdot 2 + i (- i)$

Step 2.1.2

Multiply

- 1

$- 1$ by

2

$2$ .

4 - 2 i + i \cdot 2 + i (- i)

$4 - 2 i + i \cdot 2 + i (- i)$

Step 2.1.3

Move

2

$2$ to the left of

i

$i$ .

4 - 2 i + 2 \cdot i + i (- i)

$4 - 2 i + 2 \cdot i + i (- i)$

Step 2.1.4

Multiply

$i (- i)$ .

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Step 2.1.4.1

Raise

$i$ to the power of

$1$ .

$4 - 2 i + 2 i - (i^{1} i)$

Step 2.1.4.2

Raise

$i$ to the power of

$1$ .

$4 - 2 i + 2 i - (i^{1} i^{1})$

Step 2.1.4.3

Use the power rule

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

$4 - 2 i + 2 i - i^{1 + 1}$

Step 2.1.4.4

Add

$1$ and

$1$ .

$4 - 2 i + 2 i - i^{2}$

$4 - 2 i + 2 i - i^{2}$

Step 2.1.5

Rewrite

$i^{2}$ as

$- 1$ .

$4 - 2 i + 2 i - - 1$

Step 2.1.6

Multiply

$- 1$ by

$- 1$ .

$4 - 2 i + 2 i + 1$

$4 - 2 i + 2 i + 1$

Step 2.2

Add

$4$ and

$1$ .

$5 - 2 i + 2 i$

Step 2.3

Add

$- 2 i$ and

$2 i$ .

$5 + 0$

Step 2.4

Add

$5$ and

$0$ .

$5$

$5$

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

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