Question

plz explain the formula AB=1/4{(A+B)2-(A-B}2} of algebraic identities

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Answer 1

ab=1/4(a+b)2−1/4(a−b)2ab=1/4(a+b)2−1/4(a−b)2

thus:

ab=((a+b)/2)2−((a−b)/2)2ab=((a+b)/2)2−((a−b)/2)2

I use this formula for mental calculation.
An few examples will show it's power:

19X21=202−12=400−1=39919X21=202−12=400−1=399

and

28X34=312−32=961−9=95228X34=312−32=961−9=952

Back to the formula:
ab=((a+b)/2)2−((a−b)/2)2ab=((a+b)/2)2−((a−b)/2)2

(a + b)/2 is the average of the 2 numbers to be multiplied and
(a - b)/2 is the distance of each number to the average.
In 28 X 34, 31 of course is the average and both 28 and 34 are 3 removed from 31.

This makes for very fast multiplication.
Especially so if the 2 numbers are close and if you know your squares.

°°°°°by kale~kai_zen×