In this lesson, students encounter quadratic expressions without a linear term and consider how to write them in factored form.

Students begin by studying numerical examples and noticing that expressions such as and  are equivalent. Through repeated reasoning, students are able to generalize the equivalence of these two forms as (MP8). Then, they make use of the structure relating the two expressions to rewrite expressions (MP7) from one form to the other.

Along the way, they encounter a variety of quadratic expressions that can be seen as differences of two squares, including those in which the squared term has a coefficient other than 1, or expressions that involve fractions.

Students also consider why a difference of two squares (such as  ) can be written in factored form, but a sum of two squares (such as  ) cannot be, even though both are quadratic expressions with no linear term.