Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> – y<sup>4</sup> as (x<sup>2</sup>)<sup>2</sup> – (y<sup>2</sup>)<sup>2</sup>, thus recognizing it as a difference of squares that can be factored as (x<sup>2</sup> – y<sup>2</sup>)(x<sup>2</sup> + y<sup>2</sup>).
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.