Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

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 $2$ .

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

Step 2.1.2

Multiply $- 1$ by $2$ .

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

Step 2.1.3

Multiply $2$ by $- 4$ .

$4 - 2 i - 8 i - 4 i (- i)$

Step 2.1.4

Multiply $- 4 i (- i)$ .

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Step 2.1.4.1

Multiply $- 1$ by $- 4$ .

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

Step 2.1.4.2

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

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

Step 2.1.4.3

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

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

Step 2.1.4.4

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

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

Step 2.1.4.5

Add $1$ and $1$ .

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

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

Step 2.1.5

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

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

Step 2.1.6

Multiply $4$ by $- 1$ .

$4 - 2 i - 8 i - 4$

$4 - 2 i - 8 i - 4$

Step 2.2

Subtract $4$ from $4$ .

$0 - 2 i - 8 i$

Step 2.3

Subtract $2 i$ from $0$ .

$- 2 i - 8 i$

Step 2.4

Subtract $8 i$ from $- 2 i$ .

$- 10 i$

$- 10 i$

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