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Math Help - is this correct?

  1. #1
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    is this correct?

    (1-x)9

    = 1+9x - 36x2 + 84x3 - 126x4

    not sure if the answer should begin with a plus or a minus..

    please clarify

    thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by xirokx View Post
    (1-x)9

    = 1+9x - 36x2 + 84x3 - 126x4

    not sure if the answer should begin with a plus or a minus..

    please clarify

    thanks
    Assuming you mean (1-x)^9 the first term is positive as you put.

    For every even power of x you will have a + sign and for every odd power of x will have a - sign (hence your signs are wrong from the second term onwards)

    From the binomial expansion on the first term {9 \choose 0}1^9(-x)^0 = 1
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  3. #3
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    yep i mean but dont know how to do the signs on my keyboard)

    thanks for that so is this correct now??:

    = 1+9x + 36x2 + 84x3 + 126x4

    despite having the result, what method would you use to get to the result as the method I used was the same as method I would use if calculating (1+x)7 any ideas?

    thanks for your guidance
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  4. #4
    Newbie hungthinh92's Avatar
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    What you did was wrong because (1-x)^9 must contain 9th power.

    You might use this to learn about yourself

    Binomial theorem

    Therefore, the answer should be:
    1-9x+36x^2-84x^3+126x^4-126x^5+84x^6-36x^7+9x^8-x^9
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  5. #5
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    Quote Originally Posted by xirokx View Post
    yep i mean but dont know how to do the signs on my keyboard)

    thanks for that so is this correct now??:

    = 1 - 9x + 36x2 - 84x3 + 126x4

    despite having the result, what method would you use to get to the result as the method I used was the same as method I would use if calculating (1+x)7 any ideas?

    thanks for your guidance
    See the red parts. The simplest method is to use the binomial theorem

    (a+b)^n = \sum^n_{i=0} {n \choose i}a^{n-i}b^i

    To find and given term sub in the appropriate value of i. To find the 7th term of this sequence would use n=9 and i=7
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  6. #6
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    = 1+9x + 36x2 + 84x3 + 126x4

    is that correct to the first four terms in ascending powers though? sorry didnt put that in my original post..
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  7. #7
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    Quote Originally Posted by xirokx View Post
    = 1+9x + 36x2 + 84x3 + 126x4

    is that correct to the first four terms in ascending powers though? sorry didnt put that in my original post..
    No, you need to pay more attention to your signs (also 1 is a term so you have 5 terms there )

    The first three terms are given by (1-x)^9 = {9 \choose 0}1^9(-x)^0 + {9 \choose 1}1^8(-x)^1 + {9 \choose 2}1^7(-x)^2

    Which simplifies to 1 - 9x + 36x^2
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  8. #8
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    hmmmmmmmmm


    I thought this was the answer to the first four powers in ascending order...i appreciate my signs were incorrect previously due to a typo..

    = 1-9x + 36x2 - 84x3 + 126x4
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  9. #9
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    Quote Originally Posted by xirokx View Post
    hmmmmmmmmm


    I thought this was the answer to the first four powers in ascending order...i appreciate my signs were incorrect previously due to a typo..

    = 1-9x + 36x2 - 84x3 + 126x4
    By the way you can express powers using the ^ button. Hence "x squared" is written as "x^2"

    As for that answer the first 4 terms are correct, the fifth term is also correct. I know it's a small thing but it could lose an answer mark
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  10. #10
    Super Member bigwave's Avatar
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    Quote Originally Posted by xirokx View Post
    hmmmmmmmmm


    I thought this was the answer to the first four powers in ascending order...i appreciate my signs were incorrect previously due to a typo..

    = 1-9x + 36x2 - 84x3 + 126x4
    just running it thru a calulator it is... at least it is a ck after doing the binomial therom

     <br />
(1-x)^9 =-x^9+9 x^8-36 x^7+84 x^6-126 x^5+126 x^4-84 x^3+36 x^2-9 x+1<br />
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