How do I get from:
to:
$\displaystyle (y^2+2y)^5 4(y-1)^3 = 2 \times 2 (y^2+2y)^4 (y^2+2y) (y-1)^3 = [2(y^2+2y)^4 \times (y-1)^3] \times [2 (y^2+2y)]$
$\displaystyle (y-1)^4 5(y^2+2y)^4 (2y+2) = (y-1)^3 (y-1) 5 (y^2+2y)^4 2 (y+1) = 2 (y-1)^3 (y^2+2y)^4 (y+1)$$\displaystyle = [2 (y^2+2y)^4 (y-1)^3] \times [5 (y-1) (y+1)]$
So the numerator will be :
$\displaystyle \left\{[2(y^2+2y)^4 \times (y-1)^3] \times [2 (y^2+2y)]\right\} - \left\{[2 (y^2+2y)^4 (y-1)^3] \times [5 (y-1) (y+1)]\right\}$$\displaystyle = [2 (y^2+2y)^4 \times (y-1)^3] \times [2 (y^2+2y) - 5 (y-1) (y+1)]$