Finite Math Examples

$(3 i - 6) (2 i + 5)$

Step 1

Expand $(3 i - 6) (2 i + 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 i (2 i + 5) - 6 (2 i + 5)$

Step 1.2

Apply the distributive property.

$3 i (2 i) + 3 i \cdot 5 - 6 (2 i + 5)$

Step 1.3

Apply the distributive property.

$3 i (2 i) + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

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 $3 i (2 i)$ .

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Step 2.1.1.1

Multiply $2$ by $3$ .

$6 i i + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.1.2

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

$6 (i^{1} i) + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.1.3

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

$6 (i^{1} i^{1}) + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.1.4

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

$6 i^{1 + 1} + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.1.5

Add $1$ and $1$ .

$6 i^{2} + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.2

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

$6 \cdot - 1 + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.3

Multiply $6$ by $- 1$ .

$- 6 + 3 i \cdot 5 - 6 (2 i) - 6 \cdot 5$

Step 2.1.4

Multiply $5$ by $3$ .

$- 6 + 15 i - 6 (2 i) - 6 \cdot 5$

Step 2.1.5

Multiply $2$ by $- 6$ .

$- 6 + 15 i - 12 i - 6 \cdot 5$

Step 2.1.6

Multiply $- 6$ by $5$ .

$- 6 + 15 i - 12 i - 30$

Step 2.2

Subtract $30$ from $- 6$ .

$- 36 + 15 i - 12 i$

Step 2.3

Subtract $12 i$ from $15 i$ .

$- 36 + 3 i$