Simplify (3+i)(i^2+8i-2)

$(3 + i) (i^{2} + 8 i - 2)$

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

$(3 + i) (- 1 + 8 i - 2)$

Subtract $2$ from $- 1$ .

$(3 + i) (- 3 + 8 i)$

Expand $(3 + i) (- 3 + 8 i)$ using the FOIL Method.

Apply the distributive property.

$3 (- 3 + 8 i) + i (- 3 + 8 i)$

Apply the distributive property.

$3 \cdot - 3 + 3 (8 i) + i (- 3 + 8 i)$

Apply the distributive property.

$3 \cdot - 3 + 3 (8 i) + i \cdot - 3 + i (8 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 3$ .

$- 9 + 3 (8 i) + i \cdot - 3 + i (8 i)$

Multiply $8$ by $3$ .

$- 9 + 24 i + i \cdot - 3 + i (8 i)$

Move $- 3$ to the left of $i$ .

$- 9 + 24 i - 3 \cdot i + i (8 i)$

Multiply $i (8 i)$ .

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

$- 9 + 24 i - 3 i + 8 (i^{1} i)$

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

$- 9 + 24 i - 3 i + 8 (i^{1} i^{1})$

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

$- 9 + 24 i - 3 i + 8 i^{1 + 1}$

Add $1$ and $1$ .

$- 9 + 24 i - 3 i + 8 i^{2}$

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

$- 9 + 24 i - 3 i + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$- 9 + 24 i - 3 i - 8$

Subtract $8$ from $- 9$ .

$- 17 + 24 i - 3 i$

Subtract $3 i$ from $24 i$ .

$- 17 + 21 i$