Thread: Pure Math 1 Help & Expanding trinomial

Hi,
I have a couple of homework questions, can anyone help me please?

1) Given that the expansion of (1+ax)^n begins 1+36x+576x^2, find the values of a and n.
2) Determine the coefficient of p^4q^7 in the expansion of (2p-q)(p+q)^10.

3. How to expand the entire trinomial: (10+9x³+8/(3x⁵) )³

Thank you very much

Hey ThanhPhungLe1112.

Hint for 1: What is the formula for the first three terms of a binomial expansion? Can you get results for a in terms of two of the coefficients?

um...This is what I have for number 1. I'm not sure if it's right

_nC₀ (1)ⁿ(ax)⁰ + _nC₁ (1)^n-1(ax)¹ + _nC₂ (1)^n-2(ax)²

(1)(1)(1) + _nC₁ (1) (ax) + _nC₂ (1) (a²x²)


_nC₁ (ax) = 36x
_nC₁ (a) = 36


_nC₂ (a²x²) = 576x²
_nC₂ (a²) = 576


But then from here on, I'm stuck.
Please help!
Thanks,
Phung

PS: I know that somehow you have to use the factorials formula, but I don't know how to apply it in this case.

What is the relationship between nC1 and nC2? Once you have this you will get a simple relationship between n and a that doesn't involve factorials and you can solve for n and a.

is it nC2 = nC1-n ? I'm really confused

Expand out both and simplify and try and get one in terms of a ratio and a difference.

okay, Thanks I got the answer for that problem.
But I have another assigment. So I was supposed to make a powerpoint explaining how to expand trinomials. I made my powerpoint, but when we did peer review in class this morning, some people said that I made a mistake. I can't figure out what I did wrong though so can you please help me by viewing this powerpoint and point out the mistake? I don't think it's calculation error, because I don't think they had times to check calculations so I must have solved it wrong.

This is do tomorrow so can you please help me????


* I know I made a mistake. The answer was supposed to be 1000 + 2700x^3.........
but beside that, is there anything else that I need to fix?