How do you factor x^4 - 100?

1 Answer
Nov 12, 2015

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.