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

Last Updated: 28.06.2025 14:47

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

xxxx

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

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

The Unlikely Group Getting Rich Off Dave’s Hot Chicken’s $1 Billion Deal - Forbes

xxx x

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

xxx x

As a NATO/Ukraine supporter, since you're so blown away and angered by Trump putting Zelensky in his place yesterday, why don't you support the Ukraine by joining the Ukrainian army? There's 200,000,000+ of you. Put your money where your mouths are.

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

n^2 - n + n - 1

xxx

5 daily habits suggested by top US doctor that protect the brain from early cognitive decline - Times of India

n^2 - 1

(n - 1)(n + 1)

xxx

Inflation Expectations Decline; Labor Market Expectations Improve - Federal Reserve Bank of New York

xxxx

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

Move the nub up to the top:

Thunder-Pacers: 5 takeaways as Shai Gilgeous-Alexander carries OKC to victory in Game 4 - NBA

xx