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

Last Updated: 23.06.2025 06:18

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

(n - 1)(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

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

Scientists discover universal rule that governs all life on Earth - The Brighter Side of News

xxx

xx

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

Scientists identify a group of viruses just one mutation away from causing the next pandemic - Times of India

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

xxxx

Why do Americans and foreigners alike describe the USA as prudish? Why do I see nothing prudish about the USA society? USA feels like one of the loosest countries although Americans claim to be very reserved.

xxx x

Move the nub up to the top:

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

Health officials warn of measles case from traveler at Dulles Airport - The Washington Post

xxx

xxxx

n^2 - 1

Jonas Brothers cancel and move upcoming concerts, including one in North Texas - WFAA

n^2 - n + n - 1