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

12.06.2025 13:48

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

n^2 - n + n - 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

Buried under 2 kilometers of Antarctic ice, scientists find a 34-million-year-old lost world - The Brighter Side of News

Move the nub up to the top:

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New study reveals four psychological profiles of gamers linked to mental health and attachment styles - PsyPost

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

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

June's full 'Strawberry Moon' illuminates the night sky next week: Here's how to see it - Space

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

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

Angelina Jolie And Brad Pitt’s Daughter Shiloh Reintroduces Herself With New Name - HuffPost

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n^2 - 1

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Why do most people care so much about what others think? Are they afraid of society norms?

(n - 1)(n + 1)