Simplify (-2-i)(4+i)

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Algebra

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$- 2 \cdot 4 - 2 i - i \cdot 4 - i i$

Simplify and combine like terms.

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Simplify each term.

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Multiply $- 2$ by $4$ .

$- 8 - 2 i - i \cdot 4 - i i$

Multiply $4$ by $- 1$ .

$- 8 - 2 i - 4 i - i i$

Multiply $- i i$ .

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

$- 8 - 2 i - 4 i - (i^{1} i)$

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

$- 8 - 2 i - 4 i - (i^{1} i^{1})$

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

$- 8 - 2 i - 4 i - i^{1 + 1}$

Add $1$ and $1$ .

$- 8 - 2 i - 4 i - i^{2}$

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

$- 8 - 2 i - 4 i - - 1$

Multiply $- 1$ by $- 1$ .

$- 8 - 2 i - 4 i + 1$

Add $- 8$ and $1$ .

$- 7 - 2 i - 4 i$

Subtract $4 i$ from $- 2 i$ .

$- 7 - 6 i$

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