Logo

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

12.06.2025 06:03

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

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

xxx x

xxx

New Non-Opioid Drug Offers Powerful Pain Relief Without the Dangerous Side Effects - SciTechDaily

xxxx

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

n^2 - n + n - 1

Why do flat Earthers run away like whipped dogs with their tails between their legs when asked simple questions that expose their delusions as fantasy?

xxxx

xxx

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

Wanda Sykes delivers epic 26-minute acceptance speech, mentions every other winner at event and speaks up for trans people - CNN

n^2 - 1

xxx x

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

New ‘Dungeons & Dragons’ Single-Player Video Game in the Works - Variety

(n - 1)(n + 1)

Move the nub up to the top:

xx

How can someone determine if their partner is in another romantic relationship, particularly if they do not live together?

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