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

10.06.2025 10:45

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

xxxx

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

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

Musk threatens to decommission a key space station link for NASA - AP News

n^2 - n + n - 1

Move the nub up to the top:

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

I’m a 25 year old teacher teaching at boys school & I have colleagues younger than me. I caught one of my students telling her he wanted her as his teacher instead & it hurt my feelings. They compliment her a lot. It makes me jealous. What do I do?

xx

xxx

xxx x

Samsung Nears Wide-Ranging Deal With Perplexity for AI Features - Bloomberg.com

n^2 - 1

xxxx

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

Do you think President-Elect Donald Trump won the presidency fair and square, or do you think the GOP resorted to blatant unlawful practices to tilt the election?

xxx

(n - 1)(n + 1)

xxx x

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

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