1.4.3 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.

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.

In[2]:= Factor[ % ]

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.

In[4]:= Factor[ % ]

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.

In[6]:= Expand[ % ]

Out[6]=