anonymous
  • anonymous
How do I expand: (x-i)(x+i)(x-4+i)(x-4-i)(x-2+i)(x-2-i)? Thanks in advance!
Mathematics
chestercat
  • chestercat
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BAdhi
  • BAdhi
do you see (a-b)(a+b) pattern?
anonymous
  • anonymous
You mean the (x-4-i)(x-4+i), etc.?
BAdhi
  • BAdhi
yeah.. and notice the property \((a+b)(a-b) = (a^2-b^2)\)

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anonymous
  • anonymous
Oh yeah, between the i's?
anonymous
  • anonymous
(x-i)(x+i) = (x^2-i^2) = x^ + 1?
anonymous
  • anonymous
x^2 + 1*
BAdhi
  • BAdhi
yes
anonymous
  • anonymous
Forget it, I got it,
zzr0ck3r
  • zzr0ck3r
\[\tiny (\hspace{0.2cm}x \hspace{0.2cm} - \hspace{0.2cm} i\hspace{0.2cm})\hspace{0.2cm}( \hspace{0.2cm}x\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}4\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm}\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}4\hspace{0.2cm}-\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}2\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}2\hspace{0.2cm}-\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}\]
zzr0ck3r
  • zzr0ck3r
Not what you meant?
anonymous
  • anonymous
Yeah it was @zzr0ck3r, I was able to figure it out in the end, the question asked to form a polynomial function out of the given degree and zero values using real coefficients so I just really needed help expanding it more than anything. I managed to solve it though I believe if you check my work ^ Anyway, thanks @BAdhi and @zzr0ck3r

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