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The difference is that they are both totally different things. When you times something by two you're just doubling it and when you square something you times it by itself.

Ex: 1x2=2

2x2=4

3x2=6

These are all doubling.

Ex:1 squared is the same as 1x1

2 squared is the same as 2x2

3 squared is the same as 3x3

These are all numbers squared

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