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.
<http://www.math.hmc.edu/funfacts>.
