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Math Help - Simple Binomial Expansion

  1. #1
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    Simple Binomial Expansion

    This is a two part question: First it asks to expand  (a + b)^5, and then to find the coefficient of x^3 in the expansion of  (1/4 + 2x)^5.

    I know for part one, you get  a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5, and that somehow the values of the following are substituted in this answer, but I am not really sure on how this is done or written. Could someone please help in this?
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  2. #2
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    Quote Originally Posted by db5vry View Post
    This is a two part question: First it asks to expand  (a + b)^5, and then to find the coefficient of x^3 in the expansion of  (1/4 + 2x)^5.

    I know for part one, you get  a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5, and that somehow the values of the following are substituted in this answer, but I am not really sure on how this is done or written. Could someone please help in this?
    Well in the second expansion a=\frac{1}{4} and  b=2x

    So, the coefficient of [/tex]x^3[/tex] is the 10a^2b^3 part of the expansion, just replace a and b with the values you have.
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  3. #3
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    You what the term 10a^2 b^3 where a = \frac{1}{4}\;\& \;b = 2x.
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  4. #4
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    Quote Originally Posted by Plato View Post
    You what the term 10a^2 b^3 where a = \frac{1}{4}\;\& \;b = 2x.
    So it is written as  10(1/4)^2(2x)^3, which is

     10 x 1/16 x 8
    Which is also 10 multiplied by 0.5
    Which is 5
    Making the answer  5x^3 ?
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  5. #5
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    Quote Originally Posted by db5vry View Post
    So it is written as  10(1/4)^2(2x)^3, which is

     10 x 1/16 x 8
    Which is also 10 multiplied by 0.5
    Which is 5
    Making the answer  5x^3 ?
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  6. #6
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    Quote Originally Posted by db5vry View Post
    So it is written as  10(1/4)^2(2x)^3, which is

     10 x 1/16 x 8
    Which is also 10 multiplied by 0.5
    Which is 5
    Making the answer  5x^3 ?
    Mis-use of Latex - That one line was 10 x 1/16 x 8.
    Have I got the right answer?
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