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Thread: Simple Binomial Expansion

  1. #1
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    Simple Binomial Expansion

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

    I know for part one, you get $\displaystyle a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5$, 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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    Quote Originally Posted by db5vry View Post
    This is a two part question: First it asks to expand $\displaystyle (a + b)^5$, and then to find the coefficient of $\displaystyle x^3$ in the expansion of $\displaystyle (1/4 + 2x)^5$.

    I know for part one, you get $\displaystyle a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5$, 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 $\displaystyle a=\frac{1}{4}$ and $\displaystyle b=2x$

    So, the coefficient of [/tex]x^3[/tex] is the $\displaystyle 10a^2b^3$ 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 $\displaystyle 10a^2 b^3 $ where $\displaystyle a = \frac{1}{4}\;\& \;b = 2x$.
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    Quote Originally Posted by Plato View Post
    You what the term $\displaystyle 10a^2 b^3 $ where $\displaystyle a = \frac{1}{4}\;\& \;b = 2x$.
    So it is written as $\displaystyle 10(1/4)^2(2x)^3$, which is

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

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

    $\displaystyle 10 x 1/16 x 8 $
    Which is also 10 multiplied by 0.5
    Which is 5
    Making the answer $\displaystyle 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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