Question

This is the second part of a two part question for an online class. It gave me the degree and the zeros and I had to give the factored form. I got that part right, but I need to know how to get the expanded form from the factored form. I have several more questions like this and the knowledge of how to do them would be appreciated.

Just for the record the "i"s are imaginary numbers.

Factored= 10(x-2)(x+2)(x-3i)(x+3i)

Answer 1

notice you have 2 groupings of 'difference of squares', I would do those first

10(x-2)(x+2)(x-3i)(x+3i)
= 10(x^2 - 4)(x^2 + 9)
now just slug it out ...
= 10(x^4 + 9x^2 - 4x^2 - 36)
= 10x^4 + 50x^2 - 360

let's use Wolfram to check:
http://www.wolframalpha.com/input/?i=factor+10x%5E4+%2B+50x%5E2+-+360

Yup, works

I would look for special groupings of factors like above. If you don't see any, just grind it out, one multiplication at a time.
Always simplify before doing the next multiplication.

Answer 2

Thanks for the help I really appreciate it.