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Math Help - quick question on binomial therom

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by johett View Post
    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.
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  3. #3
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    *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.
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