Difference of Squares through Pictures

factoring difference of squares through pictures

Our unit on Quadratics is probably my favorite unit to teach. There is so much growth! One of the topics we cover in our Quadratics unit is factoring differences of squares. 

I love looking at concepts through pictures (Have you seen the Pythagorean Theorem proof with water or this one with sand?). When math concepts can be shown through pictures, they seem to stick with kids longer. 

I may or may not get a little too excited about "difference of squares" literally meaning "subtract one square from another. The kids may or may not look at me like I'm crazy.

Here we have a square with side length x.

I then cut a 5x5 square out of our big square.

Now our former square has one side length x and another side length x - 5.

If we trim things to make 2 rectangles, we have a smaller rectangle with a width of 5.

Turning that rectangle on its side we now have a rectangle with side lengths x - 5 and x + 5.

I love this visual because it always works. It could even be used with graph paper so that students can count the units. 

Here is a short animation showing factoring the difference of two squares. Once students see that we really just have the difference (subtraction) of two squares, they'll begin to internalize the concept for more difficult problems.

difference of squares reference in an Algebra 1 word wall

This word wall reference for differences of squares is part of my Algebra word wall

The image above is puzzle #5 in a polynomials review digital math escape room. This one came from a teacher request. The other topics the review covers are naming polynomials, adding polynomials, subtracting polynomials, multiplying binomials and squaring binomials. 

Scaffolded Math and Science blog


  1. I love the simplistic nature of this tactile lesson for a subject that, for some young scholars, seems so abstract.

    I teach middle school scholars and also two math clubs after school; both are advanced math tutorials.

    Last year's 7th graders learned through the quadratic formula so I look forward to starting their tutorial with this exercise this year (they are now 8th graders).

    I look also forward to viewing and purchasing you lessons through TPT.


    1. Michelle, I am always blown away to hear about middle schoolers learning things I associate with older kids. It's amazing! Thank you for your comment. Math clubs sound so awesome.