Logo

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

09.06.2025 15:08

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

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

xxx x

A 'Crazy Idea' About Pluto Was Just Confirmed in a Scientific First - ScienceAlert

xxxx

n^2 - 1

(n - 1)(n + 1)

How do schizophrenia symptoms change throughout the day?

xxx

xxxx

xx

New model helps to figure out which distant planets may host life - Phys.org

Move the nub up to the top:

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

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

How do teachers justify punishing a student for fighting back against their bullies?

n^2 - n + n - 1

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

xxx x

Watch an asteroid the size of an aircraft carrier make a close pass of Earth on June 5 - Space

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