Simplify (4-i)(2+5i)

$(4 - i) (2 + 5 i)$

Step 1

Expand $(4 - i) (2 + 5 i)$ using the FOIL Method.

Apply the distributive property.

$4 (2 + 5 i) - i (2 + 5 i)$

Apply the distributive property.

$4 \cdot 2 + 4 (5 i) - i (2 + 5 i)$

Apply the distributive property.

$4 \cdot 2 + 4 (5 i) - i \cdot 2 - i (5 i)$

$4 \cdot 2 + 4 (5 i) - i \cdot 2 - i (5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $2$ .

$8 + 4 (5 i) - i \cdot 2 - i (5 i)$

Multiply $5$ by $4$ .

$8 + 20 i - i \cdot 2 - i (5 i)$

Multiply $2$ by $- 1$ .

$8 + 20 i - 2 i - i (5 i)$

Multiply $- i (5 i)$ .

Multiply $5$ by $- 1$ .

$8 + 20 i - 2 i - 5 i i$

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

$8 + 20 i - 2 i - 5 (i^{1} i)$

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

$8 + 20 i - 2 i - 5 (i^{1} i^{1})$

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

$8 + 20 i - 2 i - 5 i^{1 + 1}$

Add $1$ and $1$ .

$8 + 20 i - 2 i - 5 i^{2}$

$8 + 20 i - 2 i - 5 i^{2}$

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

$8 + 20 i - 2 i - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$8 + 20 i - 2 i + 5$

$8 + 20 i - 2 i + 5$

Add $8$ and $5$ .

$13 + 20 i - 2 i$

Subtract $2 i$ from $20 i$ .

$13 + 18 i$

$13 + 18 i$

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