Why is (n-1)(n+1)=n^2-1?
10.06.2025 19:40

xxx x
(n - 1)(n + 1)
The basic answer is that you cross-multiply the values in each factor:
U.S. economy stalled in May, Fed survey finds - MarketWatch
xxxx
xxx
Move the nub up to the top:
xxx
xxx x
n^2 - 1
Samsung could drop Google Gemini in favor of Perplexity for Galaxy S26 - Ars Technica
n^2 - n + n - 1
xx
If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2
Would you let your son wear leggings to school?
The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2
So, that’s a rectangle with sides 2 and 4.
And you are left with almost a square. One less than the square of side n.
Super-magnetic dead star throws a violent temper tantrum as NASA X-ray spacecraft looks on - Space
xxxx