Thread: quick question about cubing polynomials.

I just want to understand how you get the three when you have to cube three binomials together.



my tutor gave me this formula to follow when i come across anything I have to cube. However I'm not sure how she got the 3 there.

Originally Posted by sara213

I just want to understand how you get the three when you have to cube three binomials together.

have to cube. However I'm not sure how she got the 3 there.

Originally Posted by Plato

Thanks but that doesn't answer my question, i know that part already.

I'm talking about was the actually about the 3 in front of

Originally Posted by sara213

Thanks but that doesn't answer my question, i know that part already. I'm talking about was the actually about the 3 in front of

I beg your pardon. It actually does answer your question.
If you follow how to multiply then you know that comes from

Originally Posted by sara213

Thanks but that doesn't answer my question, i know that part already.

I'm talking about was the actually about the 3 in front of

His point is that there are terms (a)(a)(b), (a)(b)(a), and (b)(a)(a) that come up. Since there are three of them, you get a 3 in front of the .

However let's look at this differently. , right? Then you expand and simplify to get . The 2 in front of the ab appears because we have a term ab and ba.

Similarly:




Expand this and simplify. Here you will find, for instance, that you have a and a which gives you .

-Dan

The order doesn't matter in multiplication - 5*3 is the same as 3*5. This extends to letters too so and since you have three lots in your expansion it gives

If "proving" it isn't all that important look up Pascal's triangle - that gives you the coefficients necessary. Or, better yet, the binomial theorem

Okay got it...sorry plato, I did not understand what you are trying to say in the first post.