differentiating products

this is probably a really simple question seein as though its question one of the chapter!! but im not sure on how to complete it...so please help!.....the question is:

differentiate:
x^3(x-1)^2

thanks!

this is probably a really simple question seein as though its question one of the chapter!! but im not sure on how to complete it...so please help!.....the question is:

differentiate:
x^3(x-1)^2

thanks!

differentiate:
x^3(x-1)^2

Let u = x^3 ---> du/dx = 3x^2

Let v = (x-1)^2 ---> dv/dx = 2(x-1)

Hence: d/dx [x^3(x-1)^2] = u(dv/dx) + v(du/dx) = x^3[2(x-1)] + (x-1)^2[3x^2]

= x^3[2x-2] + 3x^2(x-1)(x-1)

= 2x^4 - 2x^3 + 3x^2(x^2 - 2x + 1)

= 2x^4 - 2x^3 + 3x^4 - 6x^3 + 3x^2

= 5x^4 - 8x^3 + 3x^2

---> d/dx [x^3(x-1)^2] = 5x^4 - 8x^3 + 3x^2

ok...i got that but now.....i dont get the example in the book: it goes....

Given that y=3x^3 (2x-5)^4 find dy/dx

dy/dx = v(du/dx) + u(dv/dx)

=9x^2(2x-5)^4 + 3x^3 . 8(2x-5)^3

i get that bit but then it jumps to the next step and ive dont know what they've done to get their..the next step is

= 3x^2(2x-5)^3[3(2x-5)+8x] <----how did they get this??!