To factor the expression 1 - x² completely, we can use the difference of squares formula. This formula tells us that for any two numbers a and b, the expression a² - b² can be factored as (a + b)(a - b).
In our case, a = 1 and b = x. So, we can write the expression 1 - x² as (1 + x)(1 - x).
This is the complete factorization of 1 - x². We can't factor it further because it is already in its simplest form.
Let's verify this by multiplying (1 + x)(1 - x) using the distributive property:
(1 + x)(1 - x) = 1(1) + 1(-x) + x(1) + x(-x) = 1 - x + x - x² = 1 - x²
So, our factorization is correct. The factors of 1 - x² are (1 + x) and (1 - x).
