Why does (x+1)(x-1)=x^2-1?

x² - x + x - 1 = x² - 1

Multiplication in this way is done by multiplying each term with all the other possible terms in the other brackets.

So, (a+b)(c+d) = ac+ad+bc+bd

We can try an example:

10x10 = 100

But we can write 10 as (8+2), or as (12-2)

So that means 10x10 = (8+2) x (12-2) = 8x12-8x2+2x12-2x2 = 96-16+24-4 = 100.

It works really well, but obviously in the case I showed it was pretty complicated. Because x just represents some number, we can do the same in your case.

(x+1)(x-1) = x*x-x*1+x*1-1 = x^2 - x + x - 1

But -x and x cancel, so

(x+1)(x-1) = x^2 -1