Category:Examples of Use of Difference of Two Powers

This category contains examples of use of Difference of Two Powers.

Let $\mathbb F$ denote one of the standard number systems, that is $\Z$, $\Q$, $\R$ and $\C$.

Let $n \in \N$ such that $n \ge 2$.

Then for all $a, b \in \mathbb F$:

$\ds a^n - b^n$

$=$

$\ds \paren {a - b} \sum_{j \mathop = 0}^{n - 1} a^{n - j - 1} b^j$

$\ds $

$=$

$\ds \paren {a - b} \paren {a^{n - 1} + a^{n - 2} b + a^{n - 3} b^2 + \dotsb + a b^{n - 2} + b^{n - 1} }$

Subcategories

This category has the following 2 subcategories, out of 2 total.

The following 6 pages are in this category, out of 6 total.