Basic Math Examples

$(7 i - 7) (3 - 4 i)$

Step 1

Expand $(7 i - 7) (3 - 4 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 i (3 - 4 i) - 7 (3 - 4 i)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $3$ by $7$ .

$21 i + 7 i (- 4 i) - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.2

Multiply $7 i (- 4 i)$ .

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Step 2.1.2.1

Multiply $- 4$ by $7$ .

$21 i - 28 i i - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.2.2

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

$21 i - 28 (i^{1} i) - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.2.3

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

$21 i - 28 (i^{1} i^{1}) - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.2.4

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

$21 i - 28 i^{1 + 1} - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.2.5

Add $1$ and $1$ .

$21 i - 28 i^{2} - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.3

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

$21 i - 28 \cdot - 1 - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.4

Multiply $- 28$ by $- 1$ .

$21 i + 28 - 7 \cdot 3 - 7 (- 4 i)$

Step 2.1.5

Multiply $- 7$ by $3$ .

$21 i + 28 - 21 - 7 (- 4 i)$

Step 2.1.6

Multiply $- 4$ by $- 7$ .

$21 i + 28 - 21 + 28 i$

Step 2.2

Add $21 i$ and $28 i$ .

$28 - 21 + 49 i$

Step 2.3

Subtract $21$ from $28$ .

$7 + 49 i$