Why is (n-1)(n+1)=n^2-1?

11.06.2025 04:54

Why is (n-1)(n+1)=n^2-1?

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n^2 - n + n - 1

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(n - 1)(n + 1)

Move the nub up to the top:

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So, that’s a rectangle with sides 2 and 4.

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The basic answer is that you cross-multiply the values in each factor:

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And you are left with almost a square. One less than the square of side n.

n^2 - 1

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The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

Hello, I have a question about astral projection. I started to get interested in this a little while after my mum passed in april. I thought I may be able to see her and speak with her if I managed to achieve astral projection. Since this interest, every time i sleep on my back I go into sleep paralysis. However, I cant progress into astral projection because it is very scary for me as I feel like I'm suffocating when this happens. I panic and force myself to wake up. This only ever happened about once a year before this. It sometimes lasts a long time. This has happened about 3 times per week since my mum died, as mentioned on a previous post. I no longer try to go into it anymore(due to the suffocating feeling), but it still happens. I read that sleep paralysis is the pathway to astral projection. Why has this started to happen so frequently since simply taking an interest in it? Is this connected to the afterlife? I am concerned about it as I now cannot seem to stop this happening. Could it be my mum trying to communicate? Im asking due to more knowledge around this in this group.

If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2