Question

Factor the equation and show your work.
x^2 - 1

Answer 1

`(x + 1)(x - 1)`

Explanation:

We can factor this expression using the rule:

`a^2 - b^2 = (a + b)(a - b)`

First, we can solve for a:

`x^2 = a^2`

`√(x^2) = √(a^2)`

`x = a`

Next, we can solve for b:

`1 = b^2`

`\sqrt1 = \sqrt{b^2`

`1 = b`

Finally, we can plug these a and b values into the above rule:

`(a + b)(a - b)`

`\boxed{(x + 1)(x - 1)}`