Question

How do you factor `x^4 - 100`?

Answer 1

Using the difference of squares rule.

Explanation:

The difference of squares rule means that if you have `(x^2-y^2)` you can factor it into `(x+y)(x-y)`.

Now with the equation `x^4-100` you can take the square root of `x^4` and also `100`. So the square root of `x^4` is `x^2` and the square root of `100` is `10` so you get `(x^2+10)(x^2-10)`.

Keep in mind that the difference in squares rule only works for if there is a difference (or subtraction) of two things that you can take the square root of. Now technically you could factor `x^2-10` further into `(x+sqrt(10))(x-sqrt(10))` but for the sake of this problem, I'm pretty sure you don't need to.