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Transforming Algebraic Expressions

There are often many different ways to write the same algebraic expression. As one example, the expression (1+x)2 can be written as 1+2x+x2. 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.
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Factor recovers the original form.
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It is easy to generate complicated expressions with Expand.
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Factor often gives you simpler expressions.
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There are some cases, though, where Factor can give you more complicated expressions.
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In this case, Expand gives the "simpler" form.
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