Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

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 $- 2$ by $4$ .

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

Step 2.1.2

Multiply $4$ by $- 1$ .

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

Step 2.1.3

Multiply $- i i$ .

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Step 2.1.3.1

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

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

Step 2.1.3.2

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

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

Step 2.1.3.3

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

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

Step 2.1.3.4

Add $1$ and $1$ .

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

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

Step 2.1.4

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

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

Step 2.1.5

Multiply $- 1$ by $- 1$ .

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

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

Step 2.2

Add $- 8$ and $1$ .

$- 7 - 2 i - 4 i$

Step 2.3

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

$- 7 - 6 i$

$- 7 - 6 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$