Question

How do I expand:

(x-i)(x+i)(x-4+i)(x-4-i)(x-2+i)(x-2-i)?

Thanks in advance!

Answer 1

do you see (a-b)(a+b) pattern?

Answer 2

You mean the (x-4-i)(x-4+i), etc.?

Answer 3

yeah.. and notice the property \((a+b)(a-b) = (a^2-b^2)\)

Answer 4

Oh yeah, between the i's?

Answer 5

(x-i)(x+i) = (x^2-i^2) = x^ + 1?

Answer 6

x^2 + 1*

Answer 7

yes

Answer 8

Forget it, I got it,

Answer 9

\[\tiny (\hspace{0.2cm}x \hspace{0.2cm} - \hspace{0.2cm} i\hspace{0.2cm})\hspace{0.2cm}( \hspace{0.2cm}x\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}4\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm}\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}4\hspace{0.2cm}-\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}2\hspace{0.2cm}+\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}(\hspace{0.2cm}\hspace{0.2cm}x\hspace{0.2cm}-\hspace{0.2cm}2\hspace{0.2cm}-\hspace{0.2cm}i\hspace{0.2cm})\hspace{0.2cm}\]

Answer 10

Not what you meant?

Answer 11

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