# Nth power of (a+b)

1. Jul 5, 2006

### let_me_think

can u tell me all possible ways of deriving nth power of (a+b) other than -- multiplying (a+b) again and again;binomial theorem and pascal triangle. CAN U TELL ME A FEW MORE METHODS? I'M PARTICULARLY INTERESTED IN GEOMETRICAL METHODS (someone told me there's one using PYTHAGORAS THEOREM). u may think i'm asking u a crazy question , but this is my holiday homework project for maths

2. Jul 5, 2006

### StatusX

The binomial theorem is:

$$(a+b)^n = \sum_{k=0}^n \left( \begin{array}{cc} n \\ k \end{array} \right)a^k b^{n-k}$$

Are you looking for different ways to prove this? Or different expressions equal to the LHS? Or ways of numerically computing the LHS for specific values of a and b?

3. Jul 5, 2006

### garyljc

Looks GOOD to me =) :tongue:

4. Jul 5, 2006

### Gokul43201

Staff Emeritus
I think the OP is looking for a proof of the theorem. The obvious ones are the inductive proof and some kind of combinatoric proof (I can think of one, and I imagine others of this kind are essentially the same). I can't, however, imagine a proof based on Pythgoras.

5. Jul 6, 2006

### HallsofIvy

Staff Emeritus
No, I don't think so. It seems clear that the OP is looking for different methods of finding (x+ y)n, or at least the coefficients, not just a proof of the binomial theorem. Unfortunately, I can't think of any!