Transforming Algebraic Expressions
There are often many different ways to write the same algebraic expression. As one example, the expression 
can be written as 
. Mathematica provides a large collection of functions for converting between different forms of algebraic expressions.
| Expand[expr] | multiply out products and powers, writing the result as a sum of terms |
| Factor[expr] | write expr as a product of minimal factors |
Two common functions for transforming algebraic expressions.
Expand gives the "expanded form", with products and powers multiplied out.
| Out[1]= |  |
Factor recovers the original form.
| Out[2]= |  |
It is easy to generate complicated expressions with
Expand.
| Out[3]= |  |
Factor often gives you simpler expressions.
| Out[4]= |  |
There are some cases, though, where
Factor can give you more complicated expressions.
| Out[5]= |  |
In this case,
Expand gives the "simpler" form.
| Out[6]= |  |
