I haven't done. We just started the maths course. In Chapter 1 we have so far done:
1A - Terms, Factors and indices
1B - Expanding Brackets
1C - Factorisation
1D - Algebraic Factions
1E - Four Cubic Identities. And this is where we are up to.
The answer for is given as .
So i dont' think they used complex numbers. I have tired expanding out the answer and it is correct. But i can't figure it out, how to get there?
No, it is wrong. You cannot obtain a full factorization of in .
Here is an example : someone asks you to find the solutions of . You would apply your factorization to this problem, so it becomes :
Thus we are left with :
Oops ! None of these quadratic equations admit roots in . Now you are screwed without complex numbers.
I rather think the factorization they come up with is a bit useless, since any use you would eventually make of this factorization would anyway require complex numbers to be successfully accomplished.
The question is from Cambridge Mathematics 3 Unit (year 11). Exercise 1E, question 10.
Furthermore, similar answer are given from question 11. Please have a look at http://www.mathhelpforum.com/math-he...orisation.html
So i don't know how else to figure it out with basic maths. Mind you it is from the extension question section
I know what you mean.
The factorization you are given is correct, but you will need to learn complex numbers to effectively use it to solve problems (furthermore, you will learn a much simpler factorization involving complex numbers when you will have learnt the later).
Thanks to Soroban, from post (http://www.mathhelpforum.com/math-he...orisation.html) i have figured it out:
[Difference of squares]