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Math Help - Factor each polynomial

  1. #1
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    Factor each polynomial

    I need help with these three questions,
    can someone explain to me CLEARLY how to factor each polynomial

    1. 125x^6 - 8
    2. 64x^12 - 27
    3. 8/125x^3 - 64y^6
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by skeske1234 View Post
    I need help with these three questions,
    can someone explain to me CLEARLY how to factor each polynomial

    1. 125x^6 - 8
    2. 64x^12 - 27
    3. 8/125x^3 - 64y^6
    Hi skeske1234,

    Do you know the model for factoring the difference of two cubes?

    Review this:

    x^3-y^3=(x-y)(x^2+xy+y^2)

    Apply that to your problems. First let's make them look a bit more like the difference of two cubes.

    [1] (5x^2)^3-(2)^3

    [2] (4x^4)^3-(3)^3

    [3] \left(\frac{2}{5}x\right)^3-(4y^2)^3
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  3. #3
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    Quote Originally Posted by masters View Post
    Hi skeske1234,

    Do you know the model for factoring the difference of two cubes?

    Review this:

    x^3-y^3=(x-y)(x^2+xy+y^2)

    Apply that to your problems. First let's make them look a bit more like the difference of two cubes.

    [1] (5x^2)^3-(2)^3

    [2] (4x^4)^3-(3)^3

    [3] \left(\frac{2}{5}x\right)^3-(4y^2)^3
    after you do that, how do you plug it into the formula?
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by masters View Post
    Hi skeske1234,

    Do you know the model for factoring the difference of two cubes?

    Review this:

    x^3-y^3=(x-y)(x^2+xy+y^2)

    Apply that to your problems. First let's make them look a bit more like the difference of two cubes.

    [1] (5x^2)^3-(2)^3

    [2] (4x^4)^3-(3)^3

    [3] \left(\frac{2}{5}x\right)^3-(4y^2)^3
    Quote Originally Posted by skeske1234 View Post
    after you do that, how do you plug it into the formula?
    I'll do the first one, and you see if that helps you do the other two.

    x^3-y^3=(x-y)(x^2+xy+y^2)

    In my model, let's let x=5x^2 \ \ and \ \ y=2

    (5x^2-2)\bigg((5x^2)^2+(2)(5x^2)+(2)^2\bigg)

    (5x^2-2)(25x^4+10x^2+4
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