Multiplication algorithm: Difference between revisions

Revision as of 21:26, 21 July 2023

Revision as of 21:36, 21 July 2023

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If, for example, you wanted to multiply 9 by 3, you observe that the sum and difference are 12 and 6 respectively. Looking both those values up on the table yields 36 and 9, the difference of which is 27, which is the product of 9 and 3.

==== General case ====

It can easily be proven by induction that:

<math>

xy = \frac{\left(x+y\right)^n}{2^n} - \frac{\left(x-y\right)^n}{2^n} .

</math>

====History of quarter square multiplication====