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This results in <math> xy = \frac{1}{4}((x+y)^2 - (x-y)^2)) = (p+q+\frac{1}{2})^2 - (p-q+\frac{1}{2})^2 </math>.
====Examples ====
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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, due to cansellation of cross terms, 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====
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