Canonical Forms: Evaluating and Simplifying

Factoring algebraic expressions is a technique used to break down a large expression into the product of smaller expressions. For example, $x^2+4x+4$ can be factored into $(x+2)^2$ which is more organized.

There are a few formulas that should be known which are special cases for factoring:

$x^2+2xy+y^2 = (x+y)^2$

$x^2-y^2=(x+y)(x-y)$

There is also Simon's favorite factoring trick (SFFT) which is useful in some cases of factoring:

$ax+ay+bx+by = (a+b)(x+y)$

$ax-ay-bx+by = (a-b)(x-y)$

More information on SFFT can be found here

One of the major purposes of factoring is to determine roots of equations. For example, what are the roots of $x^2+5x+6=0$? $x^2+5x+6$ can be factored into $(x+2)(x+3)$ so from here, it is clear that the roots to the equation are $x=-3, -2$.