# Thread: A simple Binomial expansion question

1. ## A simple Binomial expansion question

For the first parts of the question I had to expand $\displaystyle (1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $\displaystyle (1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\displaystyle \sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...

2. Originally Posted by JeWiSh
For the first parts of the question I had to expand $\displaystyle (1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $\displaystyle (1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\displaystyle \sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...
Those expansions are nonsense.

3. Originally Posted by Prove It
Those expansions are nonsense.
They are? They're just approximations, up to the $\displaystyle x^2$ term. The book says they're right...

4. Originally Posted by JeWiSh
They are? They're just approximations, up to the $\displaystyle x^2$ term. The book says they're right...
You should have said that when you used them.

5. Originally Posted by mr fantastic
You should have said that when you used them.
Sorry...can anyone get me started?

6. Originally Posted by JeWiSh
For the first parts of the question I had to expand $\displaystyle (1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $\displaystyle (1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\displaystyle \sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...
You mean find an approximate expression for $\displaystyle \sqrt{(1+8x)/(1-4x)}$, right .... ? To what degree?

7. Originally Posted by mr fantastic
You mean find an approximate expression for $\displaystyle \sqrt{(1+8x)/(1-4x)}$, right .... ? To what degree?
To the $\displaystyle x^2$ term I think, since that's what I was supposed to expand the original expressions to.