Simplify (3+i)(2+i)

$(3 + i) (2 + i)$

Step 1

Expand $(3 + i) (2 + i)$ using the FOIL Method.

Apply the distributive property.

$3 (2 + i) + i (2 + i)$

Apply the distributive property.

$3 \cdot 2 + 3 i + i (2 + i)$

Apply the distributive property.

$3 \cdot 2 + 3 i + i \cdot 2 + i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $2$ .

$6 + 3 i + i \cdot 2 + i i$

Move $2$ to the left of $i$ .

$6 + 3 i + 2 \cdot i + i i$

Multiply $i i$ .

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

$6 + 3 i + 2 i + i^{1} i$

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

$6 + 3 i + 2 i + i^{1} i^{1}$

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

$6 + 3 i + 2 i + i^{1 + 1}$

Add $1$ and $1$ .

$6 + 3 i + 2 i + i^{2}$

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

$6 + 3 i + 2 i - 1$

Subtract $1$ from $6$ .

$5 + 3 i + 2 i$

Add $3 i$ and $2 i$ .

$5 + 5 i$