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>).

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.