I can get the binomial theorem to work just fine when doing (a+b)^n but it becomes a problem as soon as I put coefficients, e.g.: (2a+3b)^n
Why? What is the difference and how do I calculate with coefficients?
Well, there's no difference.
$\displaystyle (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k$
$\displaystyle (2a+3b)^n = \sum_{k=0}^{n}\binom{n}{k}(2a)^{n-k}(3b)^k=\sum_{k=0}^{n}\binom{n}{k}2^{n-k}a^{n-k}\cdot 3^kb^k$
Um, did this help?
Hello, Paze!
I can get the binomial theorem to work just fine when doing $\displaystyle (a+b)^n$
but it becomes a problem as soon as I put coefficients, e.g.: $\displaystyle (2a+3b)^n$
Why? What is the difference and how do I calculate with coefficients?
Consider $\displaystyle n=3\!:\;(x+y)^3 \:=\:x^3 + 3x^2y + 3xy^2 + y^3$ .[1]
Suppose we are given: .$\displaystyle (2a + 3b)^3$
Then we have: .$\displaystyle \begin{Bmatrix}x \:=\: 2a \\ y \:=\: 3b\end{Bmatrix}$
Substitute into [1]:
. . $\displaystyle (2a + 3b)^3 \;=\;(2a)^3 +3(2a)^2(3b) + 3(2a)(3b)^2 + (3b)^3$
n . . . . . . . . $\displaystyle =\; 8a^3 + 3(4a^2)(3b) + 3(2a)(9b^2) + 27b^3$
n . . . . . . . . $\displaystyle =\;8a^3 + 36a^2b + 54ab^2 + 27b^3$
Hello, Paze!
I can get the binomial theorem to work just fine when doing
but it becomes a problem as soon as I put coefficients, e.g.:
Why? What is the difference and how do I calculate with coefficients?
Consider .[1]
Suppose we are given: .
Then we have: .
Substitute into [1]:
. .
n . . . . . . . .
n . . . . . . . .
It did indeed help. I was being silly and kept writing a^(n-k)*b^k even though I had coefficients.
Thanks a lot!
Where do I find a guide to write math like you guys do?
You can use LaTeX tags. Go to this tutorial.
[tex] x = \neg A\cdot \neg B\cdot C + \neg A\cdot B\cdot \neg C + \neg A\cdot B\cdot C + A\cdot \neg B\cdot \neg C [/tex] gives $\displaystyle x = \neg A\cdot \neg B\cdot C + \neg A\cdot B\cdot \neg C + \neg A\cdot B\cdot C + A\cdot \neg B\cdot \neg C $
Click on the “go advanced” tab. On the toolbar you will see $\displaystyle \boxed{\Sigma}$ clicking on that give the LaTeX wraps, [tex] [/tex]. The code goes between them.
You can also click on Reply with Quote. That will allow you to ‘steal’ any code that you see that you like.