Precalculus Examples

$(5 i - 3) (2 i + 1)$

Step 1

Expand $(5 i - 3) (2 i + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 i (2 i + 1) - 3 (2 i + 1)$

Step 1.2

Apply the distributive property.

$5 i (2 i) + 5 i \cdot 1 - 3 (2 i + 1)$

Step 1.3

Apply the distributive property.

$5 i (2 i) + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

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 $5 i (2 i)$ .

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Step 2.1.1.1

Multiply $2$ by $5$ .

$10 i i + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.1.2

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

$10 (i^{1} i) + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.1.3

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

$10 (i^{1} i^{1}) + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.1.4

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

$10 i^{1 + 1} + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.1.5

Add $1$ and $1$ .

$10 i^{2} + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.2

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

$10 \cdot - 1 + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.3

Multiply $10$ by $- 1$ .

$- 10 + 5 i \cdot 1 - 3 (2 i) - 3 \cdot 1$

Step 2.1.4

Multiply $5$ by $1$ .

$- 10 + 5 i - 3 (2 i) - 3 \cdot 1$

Step 2.1.5

Multiply $2$ by $- 3$ .

$- 10 + 5 i - 6 i - 3 \cdot 1$

Step 2.1.6

Multiply $- 3$ by $1$ .

$- 10 + 5 i - 6 i - 3$

Step 2.2

Subtract $3$ from $- 10$ .

$- 13 + 5 i - 6 i$

Step 2.3

Subtract $6 i$ from $5 i$ .

$- 13 - i$