In this lesson, students build a general equation for a circle. Then they revisit the distributive property as they multiply binomials. As students recognize patterns in these perfect square trinomials and squared binomials, building on their work from earlier courses, they look for regularity in repeated reasoning (MP8).

Then students rewrite perfect square trinomials in an equation that describes a circle in order to find a the center of a circle. In this lesson, the equations involve only perfect square trinomials in order to highlight that rewriting the equation in the equivalent form makes it easier to identify the center and radius of the circle.

In an upcoming lesson, students will build on these algebraic skills by completing the square to identify a circle’s radius and center, so it is not necessary to introduce that idea in this lesson.