The Average

The product of any two numbers is equal to the square of their average minus the square of their difference from average.

46 x 54 = ?

46 x 54 = 50^2 - 4^2

46 x 54 = 2500 - 16

46 x 54 = 2484

Average = (46+54)/2 = 50

Difference from average:

50-46 = 4 or 54-50 = 4

Or think of it this way:

46 is 4 below 50

54 is 4 above 50

These numbers are equally 4 below and above 50. Therefore, their average is 50 and their difference from the average is 4.

More examples:

59 x 61 = ?

59 x 61 = 60^2 - 1^2

59 x 61 = 3600 - 1

59 x 61 = 3599

73 x 87 = ?

73 x 87 = 80^2 - 7^2

73 x 87 = 6400 - 49

73 x 87 = 6351

115 x 125 = ?

115 x 125 = 120^2 - 5^2

115 x 125 = 14400 - 25

115 x 125 = 14375

394 x 406 = ?

394 x 406 = 400^2 - 6^2

394 x 406 = 160000 - 36

394 x 406 = 159964

6989 x 7011 = ?

6989 x 7011 = 7000^2 - 11^2

6989 x 7011 = 49000000 - 121

6989 x 7011 = 48999879

#Matamata