FACTOR COMPLETELY
1) x^8-y^8
Remi, Libby, Scott -- you must have a serious identity crisis.
Please use the same name for all of your posts.
Its actually 3 people, we need help with our hw , please and thank you
That having been said, you should have a clue, since you are obviously learning about factoring a difference of squares. That should be the first thing to look for. Does this look like such a beast?
Yes: x^8 - y^8 = (x^4)^2 - (y^4)^2
so the desired answer should look like
(x^4 + y^4) * (x^4 - y^4)
Whoa! Another difference of squares! If you go through the process twice more, you'll come out with the final answer.
To factor the expression x^8 - y^8 completely, we can use a special formula called the difference of squares formula.
The difference of squares formula states that for any two numbers a and b, the expression a^2 - b^2 can be factored as (a - b)(a + b).
In order to apply this formula to the expression x^8 - y^8, we need to recognize that x^8 and y^8 can be considered as the squares of two numbers: (x^4)^2 and (y^4)^2.
Using this information, we rewrite the expression as: (x^4)^2 - (y^4)^2.
Now we can apply the difference of squares formula and factor it completely as follows:
(x^4 - y^4)(x^4 + y^4).
So, the expression x^8 - y^8 can be factored as (x^4 - y^4)(x^4 + y^4).