I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.

[MathStudent2011]

I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.

I get it all correct until the simplification part.
((20)(4x+1)(-x^2+x+3)^8+(8)(1-2x)(4x+1)^5(-x^2+x+3)^7)

Which the answer states as 4(4x+1)^4(3+x-x^2)^7(17+9x-21x^2)

Can't I just divide the section where I get stuck by the LCD of 4(4x+1)^4(-x^2+x+3)^7 giving me 20x^2+8x+10 ?

[reesesloverb]

You can factor the 4(4x+1)^4(-x^2+x+3)^7 out, but you can not drop it all together. Then you are left with:

[2*(1+4x)*(1-2x)]+[5*(3+x-x^2)]

if you foil 2*(1+4x)*(1-2x) properly and the distribute and reduce, you should end up with 17+9x-21x^2 for that section and 4(4x+1)^4(3+x-x^2)^7(17+9x-21x^2) as your overall answer.