Question

Factor the following expression completely.
x4-81

Answer 1

okay, do you know how to factor? I can help you

Answer 2

\[x^{4}-81\]

Answer 3

Yes, but do you know how to factor?

Answer 4

no

Answer 5

what if that just said\[x^2-81\] would you know how to do it then?

Answer 6

it would be 9?

Answer 7

idk

Answer 8

okay, that's a good start.

Answer 9

So, you need to treat that fourth degree polynomial as just a quadratic.

Answer 10

Then what

Answer 11

We can factor a difference of fourth powers (and higher powers) by treating each term as the square of another base, using the power to a power rule. For example, to factor x 4 - y 4 , we treat x 4 as (x 2)2 and y 4 as (y 2)2 . Thus, x 4 - y 4 = (x 2)2 - (y 2)2 = (x 2 + y 2)(x 2 - y 2) = (x 2 + y 2)(x + y)(x - y) .

Answer 12

does that make sense? or do I need to explain further?

Answer 13

Yes thx.

Answer 14

let me know what you get in the end. I'll tell you if you're correct

Answer 15

To begin with, you should have\[(x^2+9)(x^2-9)\]

Answer 16

@nbarrera