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(a - b)(a + b) = a^2 - b^2

i need steps

see i^2 = -1

use FOIL on (5+8i)(5+8i)

80i-39?

then what

yes, but we usually put the "real" component first (tradition)
-39+80i

that is the b^2 in a^2 - b^2
a^2 is x^2
so the answer is
x^2 -( -39+80i) or
x^2 +39 -80 i

okay thank you so much

http://www.tiger-algebra.com/drill/(x-(5_8i)(x_(5_8i)/

because when i do it i get terms with both an i and an x and i dont know how to simplify that

painfully.
you want to do
(x^2 + (39 -80 i)) (x^2+10x-56) ?

yeah haha i tried and it just gets too confusing after awhile

no matter how you write it, it will be an ugly expression.

oh i didnt know you could do that. so should i distribute it all out?

i dont even know how to distribute the imaginary part

for the first part i got \[x ^{4}+10x ^{3}-17x ^{2}+390x-2184\]

thus we would do
(x - (5+8i))(x - (5 -8i))

wow i just realized that okay thank you

so should i foil x-5 first?

yes

okay thank youuuuuu ill tell you what i get

\[ ( x^2 -10x +89)(x-4)(x+14) \]

\[x^4-67 x^2+1450 x-4984\] looks good