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.