Algebra Examples

$(1 + i) (i + 2)$

Step 1

Expand $(1 + i) (i + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$1 (i + 2) + i (i + 2)$

Step 1.2

Apply the distributive property.

$1 i + 1 \cdot 2 + i (i + 2)$

Step 1.3

Apply the distributive property.

$1 i + 1 \cdot 2 + i i + i \cdot 2$

$1 i + 1 \cdot 2 + i i + i \cdot 2$

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 $i$ by $1$ .

$i + 1 \cdot 2 + i i + i \cdot 2$

Step 2.1.2

Multiply $2$ by $1$ .

$i + 2 + i i + i \cdot 2$

Step 2.1.3

Multiply $i i$ .

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Step 2.1.3.1

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

$i + 2 + i^{1} i + i \cdot 2$

Step 2.1.3.2

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

$i + 2 + i^{1} i^{1} + i \cdot 2$

Step 2.1.3.3

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

$i + 2 + i^{1 + 1} + i \cdot 2$

Step 2.1.3.4

Add $1$ and $1$ .

$i + 2 + i^{2} + i \cdot 2$

$i + 2 + i^{2} + i \cdot 2$

Step 2.1.4

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

$i + 2 - 1 + i \cdot 2$

Step 2.1.5

Move $2$ to the left of $i$ .

$i + 2 - 1 + 2 i$

$i + 2 - 1 + 2 i$

Step 2.2

Add $i$ and $2 i$ .

$2 - 1 + 3 i$

Step 2.3

Subtract $1$ from $2$ .

$1 + 3 i$

$1 + 3 i$

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