Logo

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

12.06.2025 05:32

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

xxx

xxxx

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

China's Tianwen 2 spacecraft sends home 1st photo as it heads for mysterious 'quasi-moon' asteroid - Space

xxx x

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

n^2 - n + n - 1

ASCO day 2: A tragic paradox, Gilead updates, and lots of Pfizer news - statnews.com

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

Move the nub up to the top:

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

These glowing axolotls may hold the secret to human limb regeneration - MSN

xx

xxxx

xxx x

Which document should be pointed out to a holocaust denier?

n^2 - 1

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

(n - 1)(n + 1)

After Drug Allegations, Elon Musk Arrives at His Own Goodbye Party With a Black Eye and a Bizarre Excuse - futurism.com

xxx