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Math Help - Factor and Simplify Algebraic Expression

  1. #1
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    Factor and Simplify Algebraic Expression

    Factor and simplify each algebraic expression.

    (4x - 1)1/2 - 1/3(4x - 1)3/2
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    Factor and simplify each algebraic expression.

    (4x - 1)1/2 - 1/3(4x - 1)3/2
    Take the factor (4x-1)^1/2 out of both parts. Get (4x-1)^1/2[1-1/3(4x-1)] etc
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    Re: Factor and Simplify Algebraic Expression

    could you further explain. I still have problems understanding why (4x - 1)1/2 - 1/3(4x - 1)3/2 = (4x-1)1/2[1-1/3(4x-1)].
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    Re: Factor and Simplify Algebraic Expression

    nevermind, figured it out, feeling real stupid right now... could you explain what to do from here.
    Last edited by PaperStSoap; June 25th 2012 at 01:59 PM.
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    nevermind, figured it out, feeling real stupid right now... could you explain what to do from here.
    Can you simplify 1 - \frac13\left(4x - 1\right)?
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    Re: Factor and Simplify Algebraic Expression

    I have no idea.
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    I have no idea.
    Are you familiar with the distributive property? Distribute the \textstyle\frac13 and combine like terms.
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    Re: Factor and Simplify Algebraic Expression

    so it comes out to 1 - 4/3x + 1/3 (4x - 1)^1/2
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    so it comes out to 1 - 4/3x + 1/3 (4x - 1)^1/2
    You need to be more careful with your parentheses, but that otherwise looks okay.

    (4x-1)^{1/2} - \frac13(4x-1)^{3/2}

    =(4x-1)^{1/2}\left[1 - \frac13(4x-1)\right]

    =(4x-1)^{1/2}\left(1 - \frac43x + \frac13\right)

    Now what is \textstyle1+\frac13?
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    Re: Factor and Simplify Algebraic Expression

    so far i got...
    (4x - 1)^1/2 (-4x/3 + 4/3)
    then i simplified (-4x/3 + 4/3) = -4x+4/3 = -4(x-1)/3
    so the it would be (4x-1)^1/2 * -4(x-1) = -4(4x-1)^1/2(x-1)
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    Factor and simplify each algebraic expression.
    (4x - 1)1/2 - 1/3(4x - 1)3/2
    Try this: let a = 4x - 1 ; then expression becomes:
    a^(1/2) - a*a^(1/2) / 3

    = [3a^(1/2) - a*a^(1/2)] / 3

    = a^(1/2)(3 - a) / 3

    continue...
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    Re: Factor and Simplify Algebraic Expression

    Quote Originally Posted by PaperStSoap View Post
    (4x - 1)^1/2 (-4x/3 + 4/3)
    then i simplified (-4x/3 + 4/3) = -4x+4/3 = -4(x-1)/3
    Again, you need to watch your parentheses. It took me a moment to realize that "-4x+4/3" was supposed to mean \textstyle\frac{-4x+4}3 and not \textstyle-4x+\frac43, which is how you wrote it.

    Quote Originally Posted by PaperStSoap View Post
    so the it would be (4x-1)^1/2 * -4(x-1) = -4(4x-1)^1/2(x-1)
    What happened to the 3?
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    Re: Factor and Simplify Algebraic Expression

    i forgot to divide the the whole thing by three. so my final answer, which is also wrong according to my book, is
    -4(4x-1)^1/2(x-1)

    the answer in the book is 4(4x-1)^1/2(x-1).

    What's tripping me up is why mine starts with -4. I must be doing something wrong when simplifying [1-1/3(4x-1)]
    where i did 1 - 1/3(4x) + 1/3(1)=
    1 - 4x/3 + 1/3 =
    3/3 - 4x/3 + 1/3 =
    -4x/3 - (3/3 + 1/3) =
    (-4x - 4)/3 =
    -4(x-1)/3
    Last edited by PaperStSoap; June 25th 2012 at 05:46 PM.
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    Re: Factor and Simplify Algebraic Expression

    Look very carefully at the original problem to make sure you've copied correctly. Is this the expression that you were given?

    (4x - 1)^{1/2} - \frac13(4x - 1)^{3/2}

    And is this the exact answer that is written in the book?

    4(4x-1)^{1/2}(x-1)

    If so, your book is in error. The correct answer would be

    -\frac43(x-1)(4x-1)^{1/2}

    or, in radical form,

    -\frac43(x-1)\sqrt{4x-1}.
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    Re: Factor and Simplify Algebraic Expression

    Double checked and I wrote it correctly. Can't believe I toiled over the wrong answer for the last hour but now I understand the process of getting the solution. Thanks for your help and being patient.
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