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Math Help - Binomial Expansion

  1. #1
    Newbie chili5's Avatar
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    Binomial Expansion

    We started doing binomial expansions today and I really do not get it at all. I get that in the form:

    (a+b)^n the exponents on a decrease and on b they increase and that there are n + 1 terms and you use pascal's triangle to get the terms but I don't quite get how to simplify what I come up with.

    E.g. (3x+4a)^5
    = 3x^5 + 5(3x^4+4a^1) + 10(3x^3+4a^2) + 10(3x^2+4a^3) + 5(3x+4a^4) + (4a^5)

    1
    1 1
    1 2 1
    1 3 3 1
    1 4 6 4 1
    1 5 10 10 5 1

    This is as far as I get but I don't get how to simplify it. Any help would be super awesome. I don't even know if that is correct.

    Thanks.
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  2. #2
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    Your expansion was not quite right, this is how is should be

    (3x+4a)^5= (3x)^5 + 5(3x)^4\times (4a)^1 + 10(3x)^3\times(4a)^2 + 10(3x)^2\times(4a)^3 + 5(3x\times(4a)^4) + (4a)^5

    Here's some help with the first 2 terms.

    (3x+4a)^5= 3^5x^5 + 5(3^4x^4\times 4a) +\dots

    (3x+4a)^5= 243x^5 + 5(81x^4\times 4a) +\dots

    (3x+4a)^5= 243x^5 + 405x^4\times 4a +\dots

    (3x+4a)^5= 243x^5 + 1620x^4a +\dots
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  3. #3
    Newbie chili5's Avatar
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    Thanks,

    when I expand it I get this:

    243x^5 + 1620x^4a + 4320x^3a^2 + 5760x^2a^3 * 3840xa^4 + 1024a^5

    Does that look right?
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  4. #4
    Master Of Puppets
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    243x^5 + 1620x^4a + 4320x^3a^2 + 5760x^2a^3 + 3840xa^4 + 1024a^5

    is correct, be careful with your signs.

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