Algebra (urgent!)

I am a bit confused about conjugates in algebra. I am supposed to multiply 8/(the square root of two + 4) by the square root of 2 -4. My math book then goes on to simplify this to (8 times the square root of two minus 32) divided by (2-4 times the square root of two plus 4 times the square root of 2 minus 16). I do not see how the bottom part came to be. Could someone offer an explanation, please?

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  1. 8/(sqrt2 + 4)
    multiply top and bottom by (sqrt 2 -4) to get rid of the sqrt on the bottom because remember:
    (a-b)(a+b) = a^2 - b^2
    thereby squaring any square roots that might have been in b
    8/(sqrt 2 + 4) * (sqrt 2-4)/(sqrt 2-4)

    = 8 (sqrt 2 - 4) / [ (sqrt 2)^2 - 16 ]

    = (8 sqrt 2 - 32) / [2-16]

    = (8 sqrt 2 - 32) / -14

    = (16 - 4 sqrt 2 / 7

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  2. By the way your math book did the
    (a-b)(a+b) by FOIL

    a^2 + ab -ab - b^2 which is a^2-b^2
    but I know and you should know that
    (a-b)(a+b) = a^2 - b^2
    without going through the FOIL

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  3. Squareroot of A* square root of AB ^2

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