<PRE><B>Question 1072494</B>
5*6 = 30 + 6 = 36 = 6^2


9 * 10 = 90 + 10 = 100 = 10^2


24 * 25 = 600 + 25 = 625 = 25^2


it appears that, if you multiply two consecutive numbers and then add the larger of the two, you will get the same result as if you squared the larger number.


this can be shown algebraically as follows:


a * (a + 1) + (a + 1) = a^2 + a + a + 1 = a^2 + 2a + 1.


factor a^2 + 2a + 1 and you will get (a + 1)^2.


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