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

Last Updated: 22.06.2025 03:06

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

xxx

xxx x

xxx

King Charles III pays respects to Air India crash victims at his annual birthday parade - PBS

(n - 1)(n + 1)

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

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

Is it possible to make cars that run on water instead of gasoline or other fossil fuels? Why haven't we done so yet?

n^2 - 1

xxx x

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

SFPD arresting dozens in 2nd night of mass protests against ICE - Mission Local

n^2 - n + n - 1

xxxx

xxxx

Mark Hughes: Mercedes can disrupt McLaren-Verstappen fight - The Race

xx

Move the nub up to the top:

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

During the Atlmark incident in 1940, the Brit war criminals violated Norwegian neutrality. Hitler could then justify invading Norway. Have the Brits ever apologized for violating Norwegian neutrality?

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