Simplify (5+i)(8+i)

$(5 + i) (8 + i)$

Step 1

Expand $(5 + i) (8 + i)$ using the FOIL Method.

Apply the distributive property.

$5 (8 + i) + i (8 + i)$

Apply the distributive property.

$5 \cdot 8 + 5 i + i (8 + i)$

Apply the distributive property.

$5 \cdot 8 + 5 i + i \cdot 8 + i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $8$ .

$40 + 5 i + i \cdot 8 + i i$

Move $8$ to the left of $i$ .

$40 + 5 i + 8 \cdot i + i i$

Multiply $i i$ .

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

$40 + 5 i + 8 i + i^{1} i$

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

$40 + 5 i + 8 i + i^{1} i^{1}$

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

$40 + 5 i + 8 i + i^{1 + 1}$

Add $1$ and $1$ .

$40 + 5 i + 8 i + i^{2}$

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

$40 + 5 i + 8 i - 1$

Subtract $1$ from $40$ .

$39 + 5 i + 8 i$

Add $5 i$ and $8 i$ .

$39 + 13 i$