# Thread: quick question on binomial therom

1. ## quick question on binomial therom

Find the general term, in simplified form...

$\displaystyle (x^2-x)^10$ (exponent 10) and $\displaystyle (a-1/a)^13$ (exponent 13)

for the first one I got an answer of $\displaystyle (10 r) x^20-r$ (exponent 20) and the second one is $\displaystyle (13 r) a^13-2r$ (exponent 13) ....but what I can't get is the $\displaystyle (-1)^r$ included for both of the answers

2. Originally Posted by johett
Find the general term, in simplified form...

$\displaystyle (x^2-x)^{10}$ and $\displaystyle (a-1/a)^{13}$

for the first one I got an answer of $\displaystyle {10\choose r} x^{20-r}$ and the second one is $\displaystyle {13\choose r} a^{13-2r}$ ....but what I can't get is the $\displaystyle (-1)^r$ included for both of the answers
One first thing: to write a long exponent, use curly brackets (like {10}) around it. You can click on the formulas in the corrected quote above to see how I changed it.

As for your question, the general formula is for $\displaystyle (a+b)^n$ but when you have $\displaystyle (a-b)^n$ (like here), this is $\displaystyle (a+(-b))^n$, hence the general term is $\displaystyle {n\choose r}a^{n-r}(-b)^r=(-1)^ra^{n-r}b^r$, hence the $\displaystyle (-1)^r$.

3. *sigh* thanks for your help!! I was stressing over this cause I have a quiz tomorrow and I wasn't sure how to get the right answers.
And thanks for showing me how to properly get the exponents.