Algebra Examples

$\frac{2 - i}{5} (i + 2)$

Step 1

Split the fraction $\frac{2 - i}{5}$ into two fractions.

$(\frac{2}{5} + \frac{- i}{5}) \cdot (i + 2)$

Step 2

Move the negative in front of the fraction.

$(\frac{2}{5} - \frac{i}{5}) \cdot (i + 2)$

Step 3

Expand $(\frac{2}{5} - \frac{i}{5}) (i + 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$\frac{2}{5} (i + 2) - \frac{i}{5} (i + 2)$

Step 3.2

Apply the distributive property.

$\frac{2}{5} i + \frac{2}{5} \cdot 2 - \frac{i}{5} (i + 2)$

Step 3.3

Apply the distributive property.

$\frac{2}{5} i + \frac{2}{5} \cdot 2 - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Combine $\frac{2}{5}$ and $i$ .

$\frac{2 i}{5} + \frac{2}{5} \cdot 2 - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Step 4.1.2

Multiply $\frac{2}{5} \cdot 2$ .

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Step 4.1.2.1

Combine $\frac{2}{5}$ and $2$ .

$\frac{2 i}{5} + \frac{2 \cdot 2}{5} - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Step 4.1.2.2

Multiply $2$ by $2$ .

$\frac{2 i}{5} + \frac{4}{5} - \frac{i}{5} i - \frac{i}{5} \cdot 2$

Step 4.1.3

Multiply $- \frac{i}{5} i$ .

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Step 4.1.3.1

Combine $i$ and $\frac{i}{5}$ .

$\frac{2 i}{5} + \frac{4}{5} - \frac{i i}{5} - \frac{i}{5} \cdot 2$

Step 4.1.3.2

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1} i}{5} - \frac{i}{5} \cdot 2$

Step 4.1.3.3

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1} i^{1}}{5} - \frac{i}{5} \cdot 2$

Step 4.1.3.4

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{1 + 1}}{5} - \frac{i}{5} \cdot 2$

Step 4.1.3.5

Add $1$ and $1$ .

$\frac{2 i}{5} + \frac{4}{5} - \frac{i^{2}}{5} - \frac{i}{5} \cdot 2$

Step 4.1.4

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

$\frac{2 i}{5} + \frac{4}{5} - \frac{- 1}{5} - \frac{i}{5} \cdot 2$

Step 4.1.5

Move the negative in front of the fraction.

$\frac{2 i}{5} + \frac{4}{5} - - \frac{1}{5} - \frac{i}{5} \cdot 2$

Step 4.1.6

Multiply $- - \frac{1}{5}$ .

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Step 4.1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{2 i}{5} + \frac{4}{5} + 1 (\frac{1}{5}) - \frac{i}{5} \cdot 2$

Step 4.1.6.2

Multiply $\frac{1}{5}$ by $1$ .

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - \frac{i}{5} \cdot 2$

Step 4.1.7

Multiply $- \frac{i}{5} \cdot 2$ .

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Step 4.1.7.1

Multiply $2$ by $- 1$ .

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - 2 \frac{i}{5}$

Step 4.1.7.2

Combine $- 2$ and $\frac{i}{5}$ .

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} + \frac{- 2 i}{5}$

Step 4.1.8

Move the negative in front of the fraction.

$\frac{2 i}{5} + \frac{4}{5} + \frac{1}{5} - \frac{2 i}{5}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{0}{5} + \frac{4}{5} + \frac{1}{5}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{0 + 4}{5} + \frac{1}{5}$

Step 4.4

Add $0$ and $4$ .

$\frac{4}{5} + \frac{1}{5}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{4 + 1}{5}$

Step 4.6

Add $4$ and $1$ .

$\frac{5}{5}$

Step 5

Divide $5$ by $5$ .

$1$