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Math Help - Binomial expansion

  1. #1
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    Binomial expansion

    the coefficient of is larger than by four times....

    i can do it easily by drawing Pascal Pyramid.....is there an equation method?

    I need help..
    Thank you
    Bizworldusa

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  2. #2
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    Re: Binomial expansion

    Mmm, look again at your post.
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  3. #3
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    Re: Binomial expansion

    Hello, bizworldusa!

    Is my interpretation correct?


    The coefficient of x^3 is larger than x^2 by four times.

    I can do it easily by drawing Pascal Pyramid. . Really? . . . How?
    Is there an equation method?

    From the title, I assume that a binomial expansion is involved
    . . and we are to determne the particular binomial.

    The simplest would be : . (ax + b)^3 \;=\;a^3x^3 + 3a^2bx^2 + 3ab^2x + b^3
    . . where a,b \ne 0.

    Then we have: . a^3 \:=\:4(3a^2b) \quad\Rightarrow\quad a^3 - 12a^2b \:=\:0

    . . . . . . . . . . a^2(a-12b) \:=\:0 \quad\Rightarrow\quad a \:=\:12b


    Therefore, one solution is: . (12x + 1)^3 \:=\:\boxed{1728}\,x^3 + \boxed{432}\,x^2 + 36x + 1


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    Of course, there is an infinite number of solutions.

    (6x+1)^4 \:=\:1296x^4 +  \boxed{864}\,x^3 + \boxed{216}\,x^2 + 24x + 1

    (4x+1)^5 \:=\:1024x^5 + 1280x^4 + \boxed{640}\,x^3 + \boxed{160}\,x^2 + 20x + 1
    Thanks from bizworldusa
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  4. #4
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    Re: Binomial expansion

    Yes your interpretation is correct mr Soroban.

    Thanks for your reply
    Bizworldusa
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