Algebra Examples

$i (2 + 3 i) (4 i - 1)$

Step 1

Apply the distributive property.

$(i \cdot 2 + i (3 i)) (4 i - 1)$

Step 2

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

$(2 \cdot i + i (3 i)) (4 i - 1)$

Step 3

Multiply $i (3 i)$ .

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Step 3.1

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

$(2 \cdot i + 3 (i^{1} i)) (4 i - 1)$

Step 3.2

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

$(2 \cdot i + 3 (i^{1} i^{1})) (4 i - 1)$

Step 3.3

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

$(2 \cdot i + 3 i^{1 + 1}) (4 i - 1)$

Step 3.4

Add $1$ and $1$ .

$(2 \cdot i + 3 i^{2}) (4 i - 1)$

Step 4

Simplify each term.

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Step 4.1

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

$(2 i + 3 \cdot - 1) (4 i - 1)$

Step 4.2

Multiply $3$ by $- 1$ .

$(2 i - 3) (4 i - 1)$

Step 5

Expand $(2 i - 3) (4 i - 1)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$2 i (4 i - 1) - 3 (4 i - 1)$

Step 5.2

Apply the distributive property.

$2 i (4 i) + 2 i \cdot - 1 - 3 (4 i - 1)$

Step 5.3

Apply the distributive property.

$2 i (4 i) + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $2 i (4 i)$ .

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Step 6.1.1.1

Multiply $4$ by $2$ .

$8 i i + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.1.2

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

$8 (i^{1} i) + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.1.3

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

$8 (i^{1} i^{1}) + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.1.4

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

$8 i^{1 + 1} + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.1.5

Add $1$ and $1$ .

$8 i^{2} + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.2

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

$8 \cdot - 1 + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.3

Multiply $8$ by $- 1$ .

$- 8 + 2 i \cdot - 1 - 3 (4 i) - 3 \cdot - 1$

Step 6.1.4

Multiply $- 1$ by $2$ .

$- 8 - 2 i - 3 (4 i) - 3 \cdot - 1$

Step 6.1.5

Multiply $4$ by $- 3$ .

$- 8 - 2 i - 12 i - 3 \cdot - 1$

Step 6.1.6

Multiply $- 3$ by $- 1$ .

$- 8 - 2 i - 12 i + 3$

Step 6.2

Add $- 8$ and $3$ .

$- 5 - 2 i - 12 i$

Step 6.3

Subtract $12 i$ from $- 2 i$ .

$- 5 - 14 i$