Chain rule: Find derivative of...?

In the answer below, I am having trouble getting from here:

= 8(1 + 4x)⁵(1 - 2x)(3 + x - x²)⁷ + 20(3 + x - x²)⁸ (1 + 4x)⁴

To here:

= 4(1 + 4x)⁴(3 + x - x²)⁷( (2)(1 + 4x)(1 - 2x) + (5)(3 + x - x²) )

Can someone explain the above step? See below for the original answer.

g(x) = (1 + 4x)⁵ (3 + x - x²)⁸

is in the form of g(x) = uv

u = (1 + 4x)⁵

du/dx = 5(4)(1 + 4x)⁴ = 20(1 + 4x)⁴

v = (3 + x - x²)⁸

dv/dx = 8(1 - 2x)(3 + x - x²)⁷

if g(x) = uv

then, g ' (x) = u dv/dx + v du/dx

g ' (x)

= (1 + 4x)⁵ (8)(1 - 2x)(3 + x - x²)⁷ + (3 + x - x²)⁸ (20)(1 + 4x)⁴

= 8(1 + 4x)⁵(1 - 2x)(3 + x - x²)⁷ + 20(3 + x - x²)⁸ (1 + 4x)⁴

= 4(1 + 4x)⁴(3 + x - x²)⁷( (2)(1 + 4x)(1 - 2x) + (5)(3 + x - x²) )

= 4(1 + 4x)⁴(3 + x - x²)⁷( (-16x² + 4x + 2) + (15 + 5x - 5x²) )

= 4(1 + 4x)⁴(3 + x - x²)⁷ (-21x² + 9x + 17)