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Math Help - Factoring Completely

  1. #1
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    Factoring Completely

    16 - 4x^4 - 4y^2 - 8x^2y

    = (-4x^4 - 4y^2 - 8x^2y) + 16
    = -4(x^4 + y^2 + 2x^2y) + 16
    = -4(x^4+y^2 + 2x^2y) + 4^2
    = 4^2 - [4(x^4 + y^2 + 2x^2y)]
    = 4^2 - [2(x+y)]^2
    = 4(2 + x^2 + y)(2 - x^2 - y)

    What I don't understand is the transition from 4^2 - [2(x+y)]^2 to 4(2 + x^2 + y)(2 - x^2 - y)

    If someone could explain it, that would be great thanks.
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  2. #2
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    Quote Originally Posted by lax600 View Post
    16 - 4x^4 - 4y^2 - 8x^2y

    = (-4x^4 - 4y^2 - 8x^2y) + 16
    = -4(x^4 + y^2 + 2x^2y) + 16
    = -4(x^4+y^2 + 2x^2y) + 4^2
    = 4^2 - [4(x^4 + y^2 + 2x^2y)]

    Mr F chips in:

    {\color{red}= 4[4 - (x^4 + y^2 + 2x^2 y)]}

    {\color{red} = 4[2^2 - (x^2 + y)^2]}

    {\color{red} = 4[A^2 - B^2]} where {\color{red}A = 2} and {\color{red}B = (x^2 + y)}

    = 4(2 + x^2 + y)(2 - x^2 - y)

    using the difference of two squares formula.

    What I don't understand is the transition from 4^2 - [2(x+y)]^2 to 4(2 + x^2 + y)(2 - x^2 - y)

    If someone could explain it, that would be great thanks.
    ..
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  3. #3
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    oh hehheh...
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