How do you factor $x^{4} - 100$ $x^4 - 100$ ?

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How do you factor $x^{4} - 100$ $x^4 - 100$ ?

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Answer 1 · 2015-11-12T23:21:12

Using the difference of squares rule.

Explanation:

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

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

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 $x^{2} - 10$ $x^2-10$ further into $(x + \sqrt{10}) (x - \sqrt{10})$ $(x+sqrt(10))(x-sqrt(10))$ but for the sake of this problem, I'm pretty sure you don't need to.

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How do you factor $x^{4} - 100$ $x^4 - 100$ ?

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