1.4.3 Transforming Algebraic ExpressionsThere 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. | |
In[1]:=
Expand[ (1 + x)^2 ]
|
Out[1]=
|
|
| Factor recovers the original form. | |
Out[2]=
|
|
| It is easy to generate complicated expressions with Expand. | |
In[3]:=
Expand[ (1 + x + 3 y)^4 ]
|
Out[3]=
|
|
| Factor often gives you simpler expressions. | |
Out[4]=
|
|
| There are some cases, though, where Factor can give you more complicated expressions. | |
In[5]:=
Factor[ x^10 - 1 ]
|
Out[5]=
|
|
| In this case, Expand gives the "simpler" form. | |
Out[6]=
|
|
|
