TITLE: Splitting out $(1-x^4)$, what is this called so I can read more about it?
QUESTION [8 upvotes]: In my calculus homework I came across a much faster* solution for one of the problems I was working on by looking at how WebAssign (online homework website) solves similar problems:
$$\lim \limits_{x \to 1} \dfrac{x(1-x^4)}{(x - 1)} = \lim \limits_{x \to 1} \dfrac{x(1-x)(1+x+x^2+x^3)}{x-1}$$ 
What is going on here, does this transformation have a name?

*this is from the problem: $$y = x - x^5$$ with the point, $P(1 , 0)$, where I couldn't find a way to solve using $$\lim \limits_{x \to a} \dfrac{f(x) - f(a)}{(x - a)}$$ so I used $$\lim \limits_{h \to 0} \dfrac{f(x + h) - f(x)}{h}$$ which required me to build a big polynomial and factor out one of the h variable)

REPLY [14 votes]: They've factored the numerator, using the ever-so-useful identity
$$x^n - 1 = (x - 1)(x^{n - 1} + x^{n - 2} + \dots + x + 1)$$

REPLY [6 votes]: It is called factorization. You can read about it here: http://en.wikipedia.org/wiki/Factorization