Real World Applications – Algebra I
Using Area Models to Factor “Special” Polynomials
The most common way to know how to factor special polynomials that are either a difference of squares or perfect square trinomials is to identify them by square roots. But how can we know how to factor them (or know which are the correct factors) once we’ve identified the trinomial as “special”?
Algebra tiles are a great tool to help students factor trinomials. First, let’s identify algebra tiles and understand what they mean.
We want to make sure that the structure we make with the algebra tiles in the polynomial is a square so it’s easy for us to factor.
I’m also going to label the sides of our rectangle. Each side of our area model is a factor in our expression!
One step further, we simplify each of the sides of this square to find the factors of this perfect square trinomial.
How do you think you can demonstrate a difference of squares using an area model? What other math concepts do you need to know in order to make this area model? (Hint: You have to know something about creating “zeros” from algebra tiles!)