Let q(x)=(x3+2x)2.
a. (a) Expand q(x) completely to express it as a polynomial in powers of x.
b. (b) By treating q(x+h)−q(x) algebraically, derive a simplified expression for hq(x+h)−q(x).
c. (c) Evaluate the limit of your result in part (b) as h→0 and obtain q′(x). Express your final answer in its most factorised form.