# How do you use the distributive property to simplify 5(6-3i)+3(i-8)?

Jun 11, 2018

$6 - 12 i$

#### Explanation:

I'm not sure if your $i$ is just a variable or if it is an imaginary number, but either way that will not affect the simplified answer.

To simplify this, use the distributive property (shown below):

Following this image, we know that:
$\textcolor{b l u e}{5 \left(6 - 3 i\right) = \left(5 \cdot 6\right) + \left(5 \cdot - 3 i\right) = 30 - 15 i}$
and
$\textcolor{b l u e}{3 \left(i - 8\right) = \left(3 \cdot i\right) + \left(3 \cdot - 8\right) = 3 i - 24}$

Now combine them:
$30 - 15 i + 3 i - 24$

Color-code the like terms:
$\textcolor{red}{30} \quad \textcolor{g r e e n}{- \quad 15 i} \quad \textcolor{g r e e n}{+ \quad 3 i} \quad \textcolor{red}{- \quad 24}$

Combine the like terms:
$6 - 12 i$

Hope this helps!