Logo

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

09.06.2025 10:33

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

xxx x

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

xxxx

Exclusive | Kimberly-Clark Nears Roughly $3.5 Billion Sale of International Tissue Business - WSJ

Move the nub up to the top:

xxx x

xxxx

Why do British people always write "xxx" after their names?

xx

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

xxx

Heads up! Midnight 16GB 13-inch M4 MacBook Air just dropped again to $800 all-time low ($199 off) - 9to5Toys

xxx

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 - 1

Sometime ago, the Iranian Minister said that a US Navy aircraft carrier would be an easy target for 300 speed boats armed with Katyusha rocket launchers. Is this true?

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

(n - 1)(n + 1)

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

Scientists measure a photonic pulse in dozens of dimensions - Earth.com

n^2 - n + n - 1