Logo

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

11.06.2025 17:57

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

xx

xxx

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

Which animal has the best sense of smell? - Live Science

xxxx

xxx x

xxx

Tuesday Telescope: Lighting, sprites, and airglow over Central America - Ars Technica

n^2 - 1

(n - 1)(n + 1)

xxxx

What are the bitter truths of life one should know?

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

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

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

Used vehicle prices ease from tariff fear-buying highs but remain elevated - CNBC

n^2 - n + n - 1

xxx x

Move the nub up to the top:

Rare Red Sprites Captured Lighting up the Tibetan Night Sky Like Jellyfish-Shaped Firework - My Modern Met

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