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Math Help - factorizing expression

  1. #1
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    factorizing expression

    Factorize

     <br /> <br />
= y^6-125 = (y^3)^2 - (5)^3<br />

    can i factorize it more? thanksss
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  2. #2
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    This is difference between two cubes:

    a^3 - b^3 = (a - b)(a^2 + ab + b^2)

    a^3 + b^3 = (a + b)(a^2 - ab + b^2)

    ===============

    y^6 - 125 = (y^2)^3 - (5)^3

    Can you do it now?
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  3. #3
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    Hello, jvignacio

    Factorize: . y^6-125

    (y^3)^2 - (5)^3 . . . . This is not factored!

    For example -- Factor: . 6x + 21

    "Factor" means to express it as a product of two or more expressins.
    . . Answer: . 3 \times (2x + 7)

    This is not factored: . (2)(3)(x) + (3)(7)
    Certainly, parts of it are factored, but it is still a sum of two expressions.



    We have: . y^6 - 125 \;=\;(y^2)^3 - (5)^3 . . . difference of cubes!

    . . You are expected to know that: . a^3 -b^3 \:=\:(a-b)(a^2 + ab +b^2)


    Therefore: . (y^2)^3 - (5)^3 \;=\;(y^2 - 5)(y^4 + 5y^2 + 25)

    Last edited by Soroban; August 21st 2008 at 09:13 AM.
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