Squaring

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When you multiply a number by itself this is called squaring

a × a = a²

An example of a square is

4 × 4 = 16

If you subtract 1 from the first number, and add 1 to the second number, you can multiply those numbers again with each other. That gives

3 × 5 = 15

That's 1 less. Would that always work? We try a larger number

10 × 10 = 100 ⇒ 9 × 11 = 99

It seems to be working again. We make a picture, and take 3 × 3 = 9 points

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We remove the bottom row and position it vertically

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Then you get 2 rows of 4 points, so 2 × 4 = 8 and there is 1 point left. That is all. Mathematically, you can write it as

x² = (x − 1)(x + 1) + 1

what you usually write in the form

x² − 1 = (x − 1)(x + 1)

That is called factorization.