Question about sum and difference of cubes

[geramul]

Hi this is my first post here. First off I want to express my immeasurable gratitude to this site as it has helped me a lot.

I have a question about as my thread title states, the sum and difference of cubes. The sample question to factor x³y⁶ – 64 confuses me. I tend to over think things in math a bit sometimes, so I'm sorry if my questions seem a bit ridiculous. Now I have two questions for this problem.

1. This one may seem silly, but I want to absolutely make sure about this. Really you can't be too careful with math now can you? the formula for sum and difference of cubes is a³ + b³ = (a + b)(a² – ab + b²), yes? Now, x³y⁶ turns into, (xy²)³. Could I have looked at this problem before as (a)(b) - (c), and therefore that is why x and y came together to become (a) - (c) as part of the factoring process?

2. My other question is why does x³y⁶ become (xy²)³? It doesn't make sense to me. I mean I understand part of the reason, but let me explain further. If I'm bringing x³y⁶ together, that should make it xy⁹, right? Now I see where the 2 and 3 are coming from, but if I try to multiply it back together I get 8 not 9. Of course I could be COMPLETELY wrong about the way I'm going about this :l.

I feel so silly not being able to figure this out.

[theshadow]

the formula for sum and difference of cubes is a³ + b³ = (a + b)(a² – ab + b²), yes? Now, x³y⁶ turns into, (xy²)³. Could I have looked at this problem before as (a)(b) - (c), and therefore that is why x and y came together to become (a) - (c) as part of the factoring process?

What do you mean by "(a)(b) - (c)"?

If I'm bringing x³y⁶ together, that should make it xy⁹, right?

No. Powers don't work that way. Look here and here.

[geramul]

I think I figured it out on my own. x³y⁶ becomes (xy²)³ because the three is getting factored out right? I hope that's right :l.