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Question:

alphadav
alphadav
Student
High School - 9th Grade

factorization of 128x4 - 54xy3

please explain with the all steps

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Posted by alphadav on Wednesday October 28, 2009 at 6:51 AM and tagged with algbrea, math.

Answers:

  1. kjcdb8er
    kjcdb8er Teacher

    eNotes Editor

    Factorization means that you take what is common between different terms, and take that out of the parenthesis grouping those terms.

    Factoring the following: 128x^4 - 54xy^3

    First, note what is common between the two terms:

    128 x^4 - 54 x y^3 =

    2*7*11 x^4 - 3*3*3*2 x y^3

    What is common between the two terms is one "2" and one "x". So take them out:

    2x(7*11 x^3 - 3^3 y^3) =

    2x(77x^3 - 27y^3)

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    Posted by kjcdb8er on Wednesday October 28, 2009 at 7:29 AM

  2. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Let A=128*x^4-54xy^3. We try to express A in as many possible factors as possible.

    2x is a factor of both terms, 128x^4 and 54xy^3.Therefore, we can write A as :

    A=2x(64x^3-27y^3)..............(1)

    We know that 64x^3 = (4x)^3    and  27y^3 = (3y)^3.

    Now let us have a transformation 4x=a and 3y=b.

    Then 64x^3-27y^3 = a^3-b^3.

    But a^3-b^3 = (a-b)(a^2+ab+b^2) is an identity.

    64x^3-27y^3 = (4x)^3-(3y)^3= (4x-3y){(4x)^2+(4x)(3x)+(3y)^2}...................(2)

    Replacing 64x^3  - 27 y^3   in  (1)  by  the expression on the right side of (2), we get:

    A=2x(4x-3y)(16x^2-12xy+9y^2)

    Therefore, 2x(4x-3y)(16x^2+12xy+9y^2) is the factor form of 128x^4-54xy^3

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    Posted by neela on Wednesday October 28, 2009 at 8:11 AM

  3. liona
    liona Teacher
    Doctorate

    From the first post,

    "First, note what is common between the two terms:

    128 x^4 - 54 x y^3 =

    2*7*11 x^4 - 3*3*3*2 x y^3

    What is common between the two terms is one "2" and one "x". So take them out:

    2x(7*11 x^3 - 3^3 y^3) =

    2x(77x^3 - 27y^3)."

    There is an error please. It should be 128x^4-54xy^3=2x(64x^3-27^3), in the first post.

    That could further be factored also.

     

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    Posted by liona on Wednesday October 28, 2009 at 8:27 AM