Question

If possible to factor the expression: x^8-1

Answer 1

think about how to factor something of the form of a difference of squares, like a^2 - b^2

Answer 2

What do you mean?

Answer 3

well, if you had x^2 - 1, could you factor it?

Answer 4

Yes? Honestly, I don't know. Math isn't my subject at all. :(

Answer 5

Have you learned this: a^2 - b^2 = (a + b)(a - b)

Answer 6

because when you multiply the right side out, you get a^2 + ab - ab - b^2

Answer 7

so you can factor x^2 - 1 like this: (x + 1)(x - 1)

Answer 8

because (x + 1)(x - 1) = x^2 + x - x - 1
= x^2 - 1

Answer 9

so for your problem, you have x^8 - 1

x^8 is like x multiplied by itself 8 times.... (x)(x)(x)(x)(x)(x)(x)(x)

so that is like (x^4)(x^4)

which is (x^4) squared...

So let's rewrite "x^8 - 1" as "x^4 squared minus 1" or "(x^4)^2 - 1"

Now it's just like the form I showed you a minute ago...

x^8 - 1 = (x^4 - 1)(x^4 + 1)

Answer 10

Yeah, you can factor it.

Answer 11

OHHHHHH MY GOODNESS!!!!! THAT MAKES SO MUCH MORE SENSE!!!!! Thank you!!! I think I'm catching on now!

Answer 12

it is a little tricky... glad you are seeing it!!! :)

Answer 13

Ok, I tried it, but the program I'm using said it was incorrect.