Differentiation Product Rule Question on $x^2(x-1)^3$

Question

I have a question:

$x^2(x-1)^3$

Which I am supposed to solve using the product rule but it seems that I have hit a dead end with the algebraic part. Here's my working so far:

$u = x^2$

$u' = 2x$

$v = (x-1)^3$

$v' = 3(x-1)^2$

$(uv)'= (x-1)^32x+x^23(x-1)^2$

This is the part I'm stuck on.

How can I move on?

Answer 1

Now, $$2x(x-1)^3+3x^2(x-1)^2=x(x-1)^2(2(x-1)+3x)=x(x-1)^2(5x-2).$$