Ok! So I think I got it...or at least I'm on the right track. Here's what I did:

Factor the expression completely.

5 * (x^2+4)^4 * (2x) * (x-2)^4 + (x^2+4)^5 * 4 * (x-2)^3

1. Find the smallest exponent I can factor out from both sides: (x^2+4)^4 and (x-2)^3 and 2 <--(Getting the 2 as the GCF of 10 and 4.)

2. Divide each term by 2 * (x^2+4)^4 * (x-2)^3 getting: 5x(x-2) + 2(x^2+4) (distributed out becomes)--> 7x^2-10x+8

3. Add the term I used to simplify the factor back in, getting a final answer of: 2 * (x^2+4)^4 * (x-2)^3 * (7x^2-10x+8)

I'm a bit confused on step 2/3. I saw that it worked...but am I really factoring out the GCF instead of dividing like I did? (Because I can't change an expression like I would an equation, having only one side.)

Thanks again for all the help. It's midnight here and I think I'm in need of a good sleep

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