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© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Easy level:

# Difference of Squares

You have all learned that

a2 - b2 = (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) = 402 - 32 = 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.

Su, Francis E., et al. "Difference of Squares." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

References:

Keywords:    lightning arithmetic, algebra
Subjects:    algebra
Level:    Easy
Fun Fact suggested by:   Francis Su
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