Basic Math Examples

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

Step 1

Expand $(28 - 4 i) (7 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$28 \cdot 7 + 28 i - 4 i \cdot 7 - 4 i i$

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 $28$ by $7$ .

$196 + 28 i - 4 i \cdot 7 - 4 i i$

Step 2.1.2

Multiply $7$ by $- 4$ .

$196 + 28 i - 28 i - 4 i i$

Step 2.1.3

Multiply $- 4 i i$ .

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Step 2.1.3.1

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

$196 + 28 i - 28 i - 4 (i^{1} i)$

Step 2.1.3.2

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

$196 + 28 i - 28 i - 4 (i^{1} i^{1})$

Step 2.1.3.3

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

$196 + 28 i - 28 i - 4 i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$196 + 28 i - 28 i - 4 i^{2}$

Step 2.1.4

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

$196 + 28 i - 28 i - 4 \cdot - 1$

Step 2.1.5

Multiply $- 4$ by $- 1$ .

$196 + 28 i - 28 i + 4$

Step 2.2

Add $196$ and $4$ .

$200 + 28 i - 28 i$

Step 2.3

Subtract $28 i$ from $28 i$ .

$200 + 0$

Step 2.4

Add $200$ and $0$ .

$200$