Question

**MEDAL FOR BEST ANSWER!!**

Answer 1

Factor this expression completely, then place the factors in the proper location on the grid.

x^6 - y^6

Answer 2

Note that both x^6 and y^6 are perfect squares. Think back to a^2 - b^2 (the difference of two squares) and how you've factored that in the past. Then do the same thing with x^6 - y^6.
If you do this correctly, you'll get two factors, each of which can be factored further.

Answer 3

Well I've tried but each time I can't get the right answer. Like so what it's (x^6-y^6)(x^2+xy+y^2)?

Answer 4

Dani: please factor a^2 - b^2 as a preliminary.

Answer 5

How do I do that?

Answer 6

Do you happen to have your math textbook available for reference? If so, try looking up "squares, difference of".

Answer 7

No. I'm homeschooled and so all my info is on a lesson online and so it's a limited amount of information. And I don't have that anywhere in the lesson.

Answer 8

All right. I'd suggest you borrow an algebra textbook from the library and use it as a reference. To solve the problem at hand, you'll need to know how to factor a^2 - b^2, as well as a^3 - b^3 and a^3 + b^3. Do you recall having seen any of these expressions before?

Answer 9

I think I remember a^3 + b^3.

Answer 10

Why not start composing a "cheat sheet" with useful formulas, for later reference and review?
To start with what looks (vaguely) familiar to you:
x^3 + y^3 factors as (x + y)(x^2 - xy + y^2).
Does that help you enough to enable you to factor x^3 - y^3?

Answer 11

Okay so how do I make that x^6 - y^6?

Answer 12

How do we factor x^3 - y^3? Since we must know how to do this to factor x^6 - y^6, please let's concentrate on factoring x^3 - y^3 first. Are you willing to give this a try?

Answer 13

Yeah isn't it (x - y) (x^2 + xy + y^2)?

Answer 14

You're right on target.
Now put all this info to use in factoring x^6 - y^6.
Since both x^6 and y^6 are perfect squares, we can re-write
x^6 - y^6 as (x^3)^2 - (y^3)^2. Can you agree to that?

Answer 15

Okay yeah. Because I can multiply the 3 by the 2 which makes it x^6-y^6.

Answer 16

OK. You already know how to factor a^2 - b^2, so please try your hand at factoring
(x^3)^2 - (y^3)^2.

Answer 17

Okay so what (x^3 - y^3) (x^2 + xy+ y^2)?

Answer 18

Your first factor, (x^3 - y^3), is correct. The second factor will be the same, except with the opposite sign.
Please try again. (x^3)^2 - (y^3)^2 factors to ... what?

Answer 19

(x^3 - y^3) (x^3 + y^3)?

Answer 20

Beautiful!

Answer 21

Now, Dani, factor each of those two factors. In other words, factor (x^3 - y^3) and (x^3 + y^3). You'll end up with four factors and thus the solution of the problem you've posed.

Answer 22

Okay so (x + y) (x - y) ( x^2 - xy -y^2) (x^2 + xy + y^2) ?

Answer 23

Too cool for words. Congratulations, Dani!!

Answer 24

Awesome! Thank you so much!

Answer 25

My great pleasure! Take care and best of luck to you!