# How do you factor x^4 - 100?

Nov 12, 2015

The difference of squares rule means that if you have $\left({x}^{2} - {y}^{2}\right)$ you can factor it into $\left(x + y\right) \left(x - y\right)$.
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 $\left({x}^{2} + 10\right) \left({x}^{2} - 10\right)$.
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 $\left(x + \sqrt{10}\right) \left(x - \sqrt{10}\right)$ but for the sake of this problem, I'm pretty sure you don't need to.