You have all learned that a^{2} – b^{2} = (a + b)(a – b)

But perhaps you haven’t thought about how to use this to do fast mental calculations! See if you can guess how this trick can help you do the following in your head:

43 x 37

78 x 82

36 x 24

Let’s do the first one. 43 x 37 = (40 + 3)(40 – 3) = 40^{2} – 3^{2} = 1600 – 9 = 1591.

Practice these, and you’ll be able to impress your friends!

**Presentation Suggestions:**

See if the class can figure out what you are about to do.

**The Math Behind the Fact:**

The moral of the story is if you think CREATIVELY about everything that you learn in mathematics, even the easy stuff like algebra, you will find some surprising applications! See more Fun Facts on lightning arithmetic, or check out the reference below.

**How to Cite this Page:**

Su, Francis E., et al. “Difference of Squares.” *Math Fun Facts*. <https://www.math.hmc.edu/funfacts>.

**References:**

A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.

**Fun Fact suggested by:**

Francis Su