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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

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.

Simplify each term.

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $- 4$ .

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

Multiply $- 4 i (- i)$ .

Multiply $- 1$ by $- 4$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

Multiply $4$ by $- 1$ .

$4 - 2 i - 8 i - 4$

$4 - 2 i - 8 i - 4$

Subtract $4$ from $4$ .

$0 - 2 i - 8 i$

Subtract $2 i$ from $0$ .

$- 2 i - 8 i$

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

$- 10 i$

$- 10 i$

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