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 ?