Challenge question: Product Rule example with factorisation! If $y=x^m(bx-c)^n$ find $y'$.

 Challenge Question:  If $y=x^m(bx-c)^n$  where $m,n$ are positive integers, and $b,c$ are non-zero real numbers, show that the first derivative equals

$$y'=\dfrac{dy}{dx}=x^{m-1}(c-bx)^{n-1}\bigg( mc -b(m+n)x\bigg)$$