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

1 Answer
Nov 12, 2015

Answer:

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.