Why is (n-1)(n+1)=n^2-1?
14.06.2025 10:34
xx
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
Your Camper’s Water Tank Could Be Carrying Serious Diseases, Here’s How To Fix It - The Autopian
n^2 - n + n - 1
The basic answer is that you cross-multiply the values in each factor:
xxx x
Solar Orbiter gets world-first views of the Sun’s poles - European Space Agency
xxx x
xxxx
xxxx
Move the nub up to the top:
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
xxx
And you are left with almost a square. One less than the square of side n.
(n - 1)(n + 1)
n^2 - 1
So, that’s a rectangle with sides 2 and 4.