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The square is 1 more than the other calculation.

The proof is quite simple: Let the numbers be x, x + 1 and x + 2

(x + 1)2 = x2 + 2x + 1;

x times x + 2 = x2 + 2x.

There is a difference of 1 whatever the value of x.

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Q: Take three consecutive numbers square the middle one and multiply the first by the third and what do you notice?
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The difference between the squares of two consecutive numbers is the sum of those two numbers. For example: 2 squared is 4. 3 squared is 9. 9-4=5 2+3=5 This is for a very simple reason: To go from 2x2 or '2 lots of two' to '3 lots of two' (3x2) we must add another two. 3 lots of two equals 2 lots of three. To get to three lots of two we need another three. We have added two then three, or 2+3. You can also apply this rule two numbers further apart, but to discover their squares' difference you must add them together and multiply by their difference EG. 2 squared is 4 4 squared is 16 16-4= 12 (2+4)x2=12