Solving Expressions: Factor a^2-b^2 and a^3-b^3

[Gus_Chiggins]

Part 1:Factor the expressions a^2-b^2 and a^3-b^3

For part 1, i worked it out to be:
(a+b)(a-b) and (a-b)(a^2+ab+b^2)

Part 2: Suppose f(x) is a function that has a derivative. Let g(x)=x^2f(x), k(x)=$$\sqrt{f(x)}$$, and p(x)=^3$$\sqrt{f(x)}$$. Without using the product rule and w/o using the chain rule, find formulas for g'(a), k'(a), and p'(a) in terms of a, f(a) and f'(a)

Any help would be great for part 2. I really don't know how to tackle this problem. Thanks!

 

[Mark44]

There was no restriction on using the limit definition of the derivative. I think that might be where they're trying to steer you, especially with the problem in part 1.