Precalculus Examples

$(2 + i) (5 + i)$

Step 1

Expand $(2 + i) (5 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 (5 + i) + i (5 + i)$

Step 1.2

Apply the distributive property.

$2 \cdot 5 + 2 i + i (5 + i)$

Step 1.3

Apply the distributive property.

$2 \cdot 5 + 2 i + i \cdot 5 + i i$

$2 \cdot 5 + 2 i + i \cdot 5 + i i$

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 $2$ by $5$ .

$10 + 2 i + i \cdot 5 + i i$

Step 2.1.2

Move $5$ to the left of $i$ .

$10 + 2 i + 5 \cdot i + i i$

Step 2.1.3

Multiply $i i$ .

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Step 2.1.3.1

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

$10 + 2 i + 5 i + i^{1} i$

Step 2.1.3.2

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

$10 + 2 i + 5 i + i^{1} i^{1}$

Step 2.1.3.3

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

$10 + 2 i + 5 i + i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$10 + 2 i + 5 i + i^{2}$

$10 + 2 i + 5 i + i^{2}$

Step 2.1.4

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

$10 + 2 i + 5 i - 1$

$10 + 2 i + 5 i - 1$

Step 2.2

Subtract $1$ from $10$ .

$9 + 2 i + 5 i$

Step 2.3

Add $2 i$ and $5 i$ .

$9 + 7 i$

$9 + 7 i$

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