Manipulation

Algebraic Manipulation

Are you a master of the kinds of algebraic manipulation you need in order to do great on the AMC?

In order to answer “yes,” you should be able to do any of the following when needed, without any hints or prompting:

• notice, and factor, a difference of squares (i.e. $x^2-y^2=(x-y)(x+y)$)
• notice, and factor, a difference or sum of cubes
• notice, and factor, a few others like that

Examples

• When you see $x^2-2xy+y^2$, do you immediately and automatically think of $(x-y{)}^2$ ?
• And do you also immediately think that adding $4xy$ to the original expression will change $(x-y{)}^2$ to $(x+y{)}^2$ ?