Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> â y<sup>4</sup> as (x<sup>2</sup>)<sup>2</sup> â (y<sup>2</sup>)<sup>2</sup>, thus recognizing it as a difference of squares that can be factored as (x<sup>2</sup> â y<sup>2</sup>)(x<sup>2</sup> + y<sup>2</sup>).
Rewrite simple rational expressions in different forms; write <sup>a(x)</sup>/<sub>b(x)</sub> in the form q(x) + <sup>r(x)</sup>/<sub>b(x)</sub>, where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*