Simplify (30-6i)(5+i)

$(30 - 6 i) (5 + i)$

Step 1

Expand $(30 - 6 i) (5 + i)$ using the FOIL Method.

Apply the distributive property.

$30 (5 + i) - 6 i (5 + i)$

Apply the distributive property.

$30 \cdot 5 + 30 i - 6 i (5 + i)$

Apply the distributive property.

$30 \cdot 5 + 30 i - 6 i \cdot 5 - 6 i i$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $30$ by $5$ .

$150 + 30 i - 6 i \cdot 5 - 6 i i$

Multiply $5$ by $- 6$ .

$150 + 30 i - 30 i - 6 i i$

Multiply $- 6 i i$ .

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

$150 + 30 i - 30 i - 6 (i^{1} i)$

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

$150 + 30 i - 30 i - 6 (i^{1} i^{1})$

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

$150 + 30 i - 30 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$150 + 30 i - 30 i - 6 i^{2}$

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

$150 + 30 i - 30 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$150 + 30 i - 30 i + 6$

Add $150$ and $6$ .

$156 + 30 i - 30 i$

Subtract $30 i$ from $30 i$ .

$156 + 0$

Add $156$ and $0$ .

$156$