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Moo · #6 April 18th, 2008, 02:37 PM

Using binomial to avoid long calculations...

If you're asked to multiply two numbers, you can rapidly go through this checking.
See if the numbers are symmetric with respect to a number N.
If so, the numbers a and b can be written as : $a=N-x$ and $b=N+x$
The product $ab$ will be :

$ab=(N-x)(N+x)$

By using a binomial formula, you get :

$ab=N^2-x^2$

Which can sometimes be more sympathical to calculate..

For example :

$58 \times 42 = ?$

Notice that these numbers are symmetric with respect to 50.

$58=50+8$
$42=50-8$

$58 \times 42 =(50+8)(50-8)=50^2-8^2=2500-64=2436$

I know that these methods look elementary, but it sometimes helps when you are in a hurry and not allowed to use any calculators

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