Why is any number squared equal to the the number before it times the number after it plus one?
Basically:
x(x+2)+1=(x+1)^2
Does this work for all numbers??
In: Mathematics
Just to pile on, multiplication is just compact notation for addition. 5*5 is a compact notation of 5+5+5+5+5. Now imagine it’s a big number and you don’t have a calculator, if you remove a 5 what happens? It goes down by 5. What happens if you change all the remaining 5s into 6s? It goes up by the number of numbers. Put it together: if you take a square, lower one factor and raise the new opposite the result is a subtraction of the original factor and addition of the exactly once lowered factor. So 5^2 minus 5 plus (5-1) is 24 or (5^2 )-1.
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