Basic Math Examples

$(7 i + 4) \cdot (2 i + 4) + (3 i) \cdot (4 i - 2)$

Step 1

Simplify each term.

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Step 1.1

Expand $(7 i + 4) (2 i + 4)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$7 i (2 i + 4) + 4 (2 i + 4) + (3 i) \cdot (4 i - 2)$

Step 1.1.2

Apply the distributive property.

$7 i (2 i) + 7 i \cdot 4 + 4 (2 i + 4) + (3 i) \cdot (4 i - 2)$

Step 1.1.3

Apply the distributive property.

$7 i (2 i) + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $7 i (2 i)$ .

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Step 1.2.1.1.1

Multiply $2$ by $7$ .

$14 i i + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.1.2

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

$14 (i^{1} i) + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.1.3

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

$14 (i^{1} i^{1}) + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.1.4

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

$14 i^{1 + 1} + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.1.5

Add $1$ and $1$ .

$14 i^{2} + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.2

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

$14 \cdot - 1 + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.3

Multiply $14$ by $- 1$ .

$- 14 + 7 i \cdot 4 + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.4

Multiply $4$ by $7$ .

$- 14 + 28 i + 4 (2 i) + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.5

Multiply $2$ by $4$ .

$- 14 + 28 i + 8 i + 4 \cdot 4 + (3 i) \cdot (4 i - 2)$

Step 1.2.1.6

Multiply $4$ by $4$ .

$- 14 + 28 i + 8 i + 16 + (3 i) \cdot (4 i - 2)$

Step 1.2.2

Add $- 14$ and $16$ .

$2 + 28 i + 8 i + (3 i) \cdot (4 i - 2)$

Step 1.2.3

Add $28 i$ and $8 i$ .

$2 + 36 i + (3 i) \cdot (4 i - 2)$

Step 1.3

Apply the distributive property.

$2 + 36 i + 3 i (4 i) + 3 i \cdot - 2$

Step 1.4

Multiply $3 i (4 i)$ .

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Step 1.4.1

Multiply $4$ by $3$ .

$2 + 36 i + 12 i i + 3 i \cdot - 2$

Step 1.4.2

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

$2 + 36 i + 12 (i^{1} i) + 3 i \cdot - 2$

Step 1.4.3

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

$2 + 36 i + 12 (i^{1} i^{1}) + 3 i \cdot - 2$

Step 1.4.4

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

$2 + 36 i + 12 i^{1 + 1} + 3 i \cdot - 2$

Step 1.4.5

Add $1$ and $1$ .

$2 + 36 i + 12 i^{2} + 3 i \cdot - 2$

Step 1.5

Multiply $- 2$ by $3$ .

$2 + 36 i + 12 i^{2} - 6 i$

Step 1.6

Simplify each term.

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Step 1.6.1

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

$2 + 36 i + 12 \cdot - 1 - 6 i$

Step 1.6.2

Multiply $12$ by $- 1$ .

$2 + 36 i - 12 - 6 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12$ from $2$ .

$- 10 + 36 i - 6 i$

Step 2.2

Subtract $6 i$ from $36 i$ .

$- 10 + 30 i$