Use the distributive property (FOIL) to simplify the expression (2-4i)(5+i). Show your work.

14 -18i

Step-by-step explanation:

(2-4i)(5+i)

FOIL

first : 2*5 =10

outer: 2*i = 2i

inner: -4i*5 = -20i

last: -4i*i = -4i^2 = -4(-1) = 4

Add these together = 10+2i -20i +4 = 14 -18i

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

40 i don’t know lololol