SOLUTION: Show that a quick way to square a positive integer ending in five is to place twenty-five after the product of the number formed by the digits preceding the five and the next integ

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Question 106191: Show that a quick way to square a positive integer ending in five is to place twenty-five after the product of the number formed by the digits preceding the five and the next integer. for example, 65(squared) = 4225 [6x7 (the next integer) =42, then tack on 25] and 125(squared) = 15,625 [12x13 (the next integer) = 156, then tack on 25].
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2B5%29%5E2=a%5E2%2B10a%2B25 Expand the right hand side.
%28a%2B5%29%5E2=%28a%5E2%2B10a%29%2B25
%28a%2B5%29%5E2=10%2A%28a%5E2%2F10%2Ba%29%2B25Distributive property.
%28a%2B5%29%5E2=10%2A10%2A%28a%5E2%2F10%5E2%2Ba%2F10%29%2B25Distributive property.
%28a%2B5%29%5E2=10%2A10%2A%28a%2F10%29%2A%28a%2F10%2B1%29%2B25Distributive property.
Example:
a=60
a%2F10=6
a%2F10%2B1=7
%28a%2B5%29%5E2=10%2A10%2A%28a%2F10%29%2A%28a%2F10%2B1%29%2B25
%2860%2B5%29%5E2=10%2A10%2A%2860%2F10%29%2A%2860%2F10%2B1%29%2B25
65%5E2=100%2A6%2A7%2B25
4225=4225