quick question on binomial therom

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November 6th 2008, 11:08 AM
johett

quick question on binomial therom

Find the general term, in simplified form...

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

for the first one I got an answer of $(10 r) x^20-r$ (exponent 20) and the second one is $(13 r) a^13-2r$ (exponent 13) ....but what I can't get is the $(-1)^r$ included for both of the answers
November 6th 2008, 12:00 PM
Laurent

Quote:

Originally Posted by johett

Find the general term, in simplified form...

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

for the first one I got an answer of ${10\choose r} x^{20-r}$ and the second one is ${13\choose r} a^{13-2r}$ ....but what I can't get is the $(-1)^r$ 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 $(a+b)^n$ but when you have $(a-b)^n$ (like here), this is $(a+(-b))^n$ , hence the general term is ${n\choose r}a^{n-r}(-b)^r=(-1)^ra^{n-r}b^r$ , hence the $(-1)^r$ .
November 6th 2008, 12:12 PM
johett

(Happy)(Happy)(Happy) *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.