# Thread: Binomial Expansion Query

1. ## Binomial Expansion Query

Hi,

I'm happy enough expanding easy binomial questions, e.g. Expanding $\displaystyle (x + 2)^7$

I have a query though about something the teacher said today that I was hoping if somebody could tell me why you would need to do what they said;

"If you have the x term on the left, e.g $\displaystyle (2x + 1)^6$ or $\displaystyle (\frac{1}{x} - 5)^{12}$ always move it to the right, so those would become $\displaystyle (1 + 2x)^6$ and $\displaystyle (-5 + \frac{1}{x})^{12}$"

As far as I can see, wouldn't you get the same answer either way?

Thanks in advance for any help, I'm interested to know why this would be necessary and in which cases would it give a different answer?

2. Originally Posted by Markus123
"If you have the x term on the left, e.g $\displaystyle (2x + 1)^6$ or $\displaystyle (\frac{1}{x} - 5)^{12}$ always move it to the right, so those would become $\displaystyle (1 + 2x)^6$ and $\displaystyle (-5 + \frac{1}{x})^{12}$"
As far as I can see, wouldn't you get the same answer either way?
And why not?
$\displaystyle \sum\limits_{k = 0}^N {{N \choose k} x^k y^{N - k} = \sum\limits_{k = 0}^N { N \choose k } y^k x^{N - k} }$
Recall that $\displaystyle { N \choose k } = { N \choose N-k }$
Try some examples.

3. I tried it with quite a few questions both ways and always got the same answer and hopefully, if I understand your post correctly (I'm not very good at Maths so I might not ) you confirm it would get the same answer both ways.

If that is the case do you know why the teacher would be telling us to move the x term to the right?

thanks for the reply.

4. Originally Posted by Markus123
If that is the case do you know why the teacher would be telling us to move the x term to the right?
Why do you not simply show your teacher this thread?