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?

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- Jan 12th 2013, 02:35 AMPazeBinomial Theorem with coefficients
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? - Jan 12th 2013, 05:45 AMveileenRe: Binomial Theorem 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? - Jan 12th 2013, 08:02 AMSorobanRe: Binomial Theorem with coefficients
Hello, Paze!

Quote:

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 . . . . . . . . $\displaystyle =\;8a^3 + 36a^2b + 54ab^2 + 27b^3$

- Jan 12th 2013, 02:06 PMPazeRe: Binomial Theorem with coefficientsQuote:

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? :) - Jan 12th 2013, 02:29 PMPlatoRe: Binomial Theorem with coefficients

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.