AFAIK algebraic simplification isn't the same as factorisation. Though its one of those maths definition that I don't like so much.
Cartoon Corpse said:
k/3(kk+3k+2) + (kk+3k+2)
= 1/3( k(kk+3k+2) + 3(kk+3k+2))
That doesn't equal. How did you end up with 3(kk+3k+2) ?
doesn't the 1/3 go away when you multiply the whole line by 3 (simplifier). so you end up with just k**3 + 6k**2 + 11k + 6?
You can only do that if the original question is (1/3)k(k+1)(K+2) + (k+1)(K+2) = 0, but it isn't so you can't.
I'll do it for Killer sake. Here is my version of it, take it as you will. Simplification in algebra is collecting like terms, its different from factorising. So if you are given something in factorised form, expand it out and afterward put the like terms together by addition or subtraction.
(1/3)k(k+1)(k+2) + (k+1)(k+2)
= (1/3)k(k^2 + 2k + k + 2) + (k^2 + 2k + k + 2)
= (1/3)k(k^2 + 3k + 2) + (k^2 + 3k + 2)
= (1/3)(k^3 + 3k^2 + 2k) + (k^2 + 3k + 2)
= 1/3k^3 + k^2 + 2/3k + k^2 + 9/3k + 2 (edited)
= 1/3k^3 + 2k^2 + 11/3k + 2 (edited)
There you go.
Edit: Sorry I made a typo on the second last line that lead to an error in the final line.