Suppose we square several binomials, or expressions that contain 2 terms. We get trinomials, or expressions that contain 3 terms. Does any pattern emerge in the results?

Each of the expressions on the right is called a perfect square trinomial because it is the result of multiplying an expression by itself. There is a pattern in the results: When the coefficient of  in a trinomial is 1, if the constant term is the square of half the coefficient of , then the expression is a perfect square trinomial.

For example, is a perfect square trinomial because the constant term, 49, can be rewritten as (-7)², and half of -14 is -7. This expression can be rewritten as a squared binomial: .

Two squared binomials show up in the equation for circles: . Equations for circles are sometimes written in different forms, but we can rearrange them to help find the center and radius of the circle. For example, suppose the equation of a circle is written like this:

We can’t immediately identify the center and radius of the circle. However, if we rewrite the two perfect square trinomials as squared binomials and rewrite the right side in the form , the center and radius will be easier to recognize.

The first 3 terms on the left side, , can be rewritten as . The remaining terms, , can be rewritten as . The right side, 225, can be rewritten as 15². Let’s put it all together.

Now we can see that the center of the circle is , and the circle’s radius measures 15 units.