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Math Help - Expanding and subtracting binomials

  1. #1
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    Expanding and subtracting binomials

    I'm working on expanding binomials and I currently understand how to expand basic ones using the binomial theorem. But due to transferring to my Precalc class late, I missed the lecture on them. Could someone explain how to expand and simplify this expression using the binomial theorem?

    2(x-3)^4 + 5(x-3)^2

    Thanks in advance!
    Last edited by zsf1990; January 20th 2013 at 05:07 PM.
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    Re: Expanding and subtracting binomials

    Quote Originally Posted by zsf1990 View Post
    I'm working on expanding binomials and I currently understand how to expand basic ones using the binomial theorem. But due to transferring to my Precalc class late, I missed the lecture on them. Could someone explain how to expand and simplify this expression using the binomial theorem?

    2(x-3)^4 + 5(x-3)^2

    Thanks in advance!

    OH, Come on!
    2(x-3)^4 + 5(x-3)^2=(x-3)^2[2(x-3)^2+5][
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    Re: Expanding and subtracting binomials

    I don't think I understand what you mean. The book gives 2x^4-24x^3+113x^2-246x+207 as the solution. I got 2x^4 - 8x^3 3 + 17x^2 9 - 14x27 + 126 by applying the 2 and 5 after expanding, then combining like terms. I'm not sure where I messed up.
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    Re: Expanding and subtracting binomials

    Quote Originally Posted by zsf1990 View Post
    I don't think I understand what you mean. The book gives 2x^4-24x^3+113x^2-246x+207 as the solution. I got 2x^4 - 8x^3 3 + 17x^2 9 - 14x27 + 126 by applying the 2 and 5 after expanding, then combining like terms. I'm not sure where I messed up.
    May I ask you, if you know the answer then why are you asking?
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    Re: Expanding and subtracting binomials

    Knowing the answer does me no good if I don't know how to get there. I know how to expand the binomial (x - 3)^4 and how to subtract the two expanded terms. What I don't understand is what to do with the 2 and the 5.
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    Re: Expanding and subtracting binomials

    Quote Originally Posted by zsf1990 View Post
    Knowing the answer does me no good if I don't know how to get there. I know how to expand the binomial (x - 3)^4 and how to subtract the two expanded terms. What I don't understand is what to do with the 2 and the 5.
    Once you expand each of the terms using the Binomial Theorem, multiply each term through by 2 or 5 (depending on which number is out the front).

    However, Plato's advice gives you an easier alternative form to work with.
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