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

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Answer 1 · 2018-06-11T05:19:17

#6 - 12i#

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):
cdn.virtualnerd.com

Following this image, we know that:
#color(blue)(5(6-3i) = (5 * 6) + (5 * -3i) = 30 - 15i)#
and
#color(blue)(3(i-8) = (3 * i) + (3 * -8) = 3i - 24)#

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

Color-code the like terms:
#color(red)(30) quadcolor(green)(-quad15i) quadcolor(green)(+quad3i) quadcolor(red)(-quad24)#

Combine the like terms:
#6 - 12i#

Hope this helps!