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Math Help - Algebra 2 help

  1. #1
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    Exclamation Algebra 2 help

    find the product (a-1)^4. ive tried this problem 4 times and i keep getting the answer wrong
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  2. #2
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    Quote Originally Posted by racerfreak05 View Post
    find the product (a-1)^4. ive tried this problem 4 times and i keep getting the answer wrong
    Binomial theorem.

     \displaystyle (a-1)^4 = \sum_{k=0}^{4} \tbinom nka^{n-k}(-1)^k

    =  \tbinom 40 a^{4}(-1)^0 +  \tbinom 41 a^{3}(-1)^1+  \tbinom 42 a^{2}(-1)^2+  \tbinom 43 a^{1}(-1)^3+  \tbinom 44 a^{0}(-1)^4

    where  \tbinom nk = \frac{n!}{k!\,(n-k)!}
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  3. #3
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    Another option other than what Mush posted would be to take (a-1)(a-1)(a-1)(a-1)
    =(a^2 - 2a +1)(a-1)(a-1)
    =(a^3 -2a^2+a-a^2+2a-1)(a-1)
    =(a^3-3a^2+3a-1)(a-1)
    =a^4-4a^3+6a^2-4a+1

    Hopefully this will help you out a little bit. Basically what you are looking to do is use the distributive property and "FOIL" the (a-1)'s out on each other.
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